Basic and advanced grade 5 triangle problems

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Ngày cập nhật gần nhất: 15/4/2026

Content

1. Grade 5 triangle problems in Textbooks

2. Grade 5 triangle problem in Workbook

3. Grade 5 triangle problems with answers

Explore basic and advanced grade 5 triangle problems along with detailed and specific solutions for each, students in grade 5 who want to study Mathematics can refer to and do exercises as well as compare with solutions to effectively learn triangle Mathematics, reinforce triangle area and perimeter knowledge.

Triangle problems are one of the important knowledge areas, appearing in tests, mid-term exams, and end-of-term exams, so studying theory as well as solving exercises on basic and advanced grade 5 triangle problems is very necessary. Here are some advanced and basic grade 5 triangle problems, students can refer to them to know more problem types and solve them effectively.

Basic and advanced triangle problems

Attention: Refer to the formula for triangle area before applying it to the exercise; Triangle area is measured in m², dm², cm² ...

Article Contents:
1. Exercises in Textbooks.
2. Exercises in Exercise Books.
3. Advanced Exercises.

1. Grade 5 triangle problems in Textbooks

Exercise 1 Page 88 Textbook Math 5: Calculate the area of a triangle with:

a) The length of the base is 8cm and the height is 6cm.
b) The length of the base is 2.3dm and the height is 1.2dm.

Answer:

Exercise 2 Page 88 Textbook Math 5: Calculate the area of a triangle with:

a) The length of the base is 5m and the height is 24dm.
b) The length of the base is 42.5m and the height is 5.2m.

Exercise 1 Page 86 Textbook Math 5: List the names of three angles and three sides of each triangle below:

Answer:

Exercise 2 Page 86 Textbook Math 5: Identify the base and corresponding altitude drawn in each triangle below:

Answer:
Triangle ABC has: Base AB, altitude CH
Triangle DEG has: Base EG, altitude DK
Triangle PQM has: Base PQ, altitude MN

Exercise 3 Page 86 Textbook Math 5: Compare the area of triangles:

Answer:
a) Area of triangle AED = Area of triangle EDH.
b) Area of triangle EBC = Area of triangle EHC.
c) Rectangle ABCD = Area of triangle EDC.

Attention: Refer to Grade 5 triangle area problem solutions for suitable solving methods, accurate exercise completion, and ease of use.

2. Grade 5 triangle problem in Workbook

3. Grade 5 triangle problems with answers

Exercise 1: A triangle has a base of 15 cm and a height of 2.4 cm. Find the area of this triangle?

Solution:

The area of the triangle is:

15 x 2.4 : 2 = 18 (cm²)

Answer: 18cm²

Exercise 2: A triangle has a base of 12cm and a height of 25mm. Find the area of this triangle?

Solution:

Convert: 25mm = 2.5 cm

The area of this triangle is:

12 x 2.5 : 2 = 15 (cm²)

Answer: 15cm²

Exercise 3: A triangular tomb has an area of 129m² and a height of 24m. What is the length of its base?

Solution:

The length of its base is:

129 x 2 : 24 = 10.75 (m)

Answer: 10.75m

Exercise 4: A triangular billboard has a sum of base and height equal to 28m, with the base being 12m longer than the height. Find the area of the billboard.

Solution:

The length of the base is:

(28 + 12) : 2 = 20 (m)

The length of the height is:

28 - 20 = 8 (m)

The area of the billboard is:

20 x 8 : 2 = 80 (m2)

The answer is: 80m2

Exercise 5: A rectangle has an area of 630cm2, which is equal to 70% of the area of a triangle. Calculate the base of the triangle, knowing that the height is 2.4dm.

Solution:

Convert: 2.4dm = 24cm

The area of the triangle is:

630 : 70% = 900 (cm2)

The base of the triangle is:

900 x 2 : 24 = 75 (cm)

The answer is: 75cm

Exercise 6: A rectangular sheet of paper has an area of 60464mm2 and this area is equal to 4/3 of the area of a triangular sheet of paper. Calculate the base of the triangular sheet of paper, knowing that the height of the paper is 24cm?

Solution:

Change 24cm to 240mm

The area of the triangle is:

60464 : 4/3 = 45348 (mm2)

The base of the triangular sheet of paper is:

45348 x 2 : 240 = 377.9 (mm)

Answer: 377.9mm

Problem 7: Given right triangle ABC with angle B, the perimeter is 37dm. Side AB is 2/3 of side AC, and side BC is 4/5 of side AC. Calculate the area of triangle ABC.

Solution:

We have: 2/3 = 10/15 and 4/5 = 12/15

If side AC is divided into 15 equal parts, then side AB is 10 parts and BC is 12 parts accordingly.

The length of side AB is:

37 : (15 + 10 + 12) x 10 = 10 (dm)

The length of side AC is:

37 : (15 + 10 + 12) x 15 = 15 (dm)

The length of side BC is:

37 - 10 - 15 = 12 (dm)

The area of triangle ABC is:

10 x 12 : 2 = 60 (dm2)

The answer is: 60dm2

Exercise 8: Given right triangle ABC at A, with a perimeter of 90cm. Side AB equals 4/3 of side AC, and side BC equals 5/3 of side AC. Find the area of triangle ABC?

Solution:

Side AC is divided into 3 equal parts, then side AB is 4 parts, and side BC is 5 parts like that.

The length of side AB is:

90 : (3 + 4 + 5) x 4 = 30 (cm)

The length of side AC is:

90 : (3 + 4 + 5) x 3 = 22.5 (cm)

The area of triangle ABC is:

30 x 22.5 : 2 = 337.5 (cm2)

Answer: 337.5 cm2

Exercise 9: A triangular plot of land has a height of 10 m. If the base is extended by another 4 m, how much will the area increase?

Solution:

If the base is extended by 4m, the area will increase by:

The area of triangle ABC is:

Answer: 20m2

Exercise 10: A triangle ABC has a base length of 3.5m. If the base BC is extended by 2.7m, the area of the triangle increases by 5.265 m2. Calculate the area of triangle ABC.

Solution:

The height of the triangle is:

10.72 feet

The area of triangle ABC is:

23.45 square meters

Answer: 6.825 square meters

Exercise 11: Given the area of rectangle ABCD is 2400 cm2

Calculate the area of triangle MDC?

Solution:

CD = 2400 : (25 + 15) = 60 centimeters

Area of triangle MDC = (60 x 25) : 2 = 750 square centimeters

Exercise 12: Given triangle ABC with area = 150 square centimeters. If extending base BC (towards B) by 5 cm, the area will increase by 37.5 square centimeters. Calculate the base BC of the triangle.

Solution:

From A, drop perpendicular AH to CD, AH is the common height of triangles ABC and ABD. AH length is: (37.5 x2) : 5 = 15 centimeters

Base BC is: (150 x2) : 15 =20 centimeters

Exercise 13: Given triangle ABC with area of 150 square centimeters. Extend BC to point CD such that CD = 1/3 BC.

a. Calculate the area of triangle ACD

b. On AC, take E and F such that AE = EF = FC. Compare the areas of triangles ABE, BEF, BCF

Solution:

a. Considering triangles ABC and ACD, observing they have the same altitude drawn from vertex A and CD = 1/3 BC, hence:

SACD = 1/3. SABC = 1/3. 150 = 50 square centimeters

b. Considering 3 triangles ABE, EBF, and FBC, observing they share a common altitude drawn from vertex B and AE = EF = FC so SABE = SBEF = SBCF = SACD = 1/3. SABC

Exercise 14: Given triangle ABC, D is the midpoint of side BC, E is the midpoint of side AC. Two straight lines AD and BE intersect at I. Compare the areas of triangles AIE and BID.

Solution:

Considering triangles ABD and ABC, we have:

- Sharing the same altitude from A

- BC = 2 times BD

Consequently: SABC = 2 times SABD

Considering triangles ABC and ABE, we have:

- Sharing the same altitude from B

- AC = 2 times AE

Consequently: SABC = 2 times SABE

So SABD = SABE

SABI + SAIE = SABI + SBID

SAIE = SBID

2. Triangle Exercises

Question 1: The area of a rectangular sheet is 604.64 square centimeters and equals 4/3 of the area of a triangle. Calculate the base of the triangle sheet, knowing the height of the sheet is 24 cm.

Question 2: A triangular piece of land has a total of the two perpendicular sides measuring 62cm. One of these perpendicular sides is one and a half times the length of the other. Calculate the area of the piece of land.

Question 3: Calculate the perimeter and area of a right triangle with one perpendicular side measuring 24 cm and equals 3/4 of the other perpendicular side. The remaining side is 40cm long.

Question 4: A garden plot is a right-angled triangle ABC with right angle at A. Side AC is 30m longer than side AB. Side BC measures 150m.

a) Calculate the lengths of sides AB and AC. Knowing the perimeter of the plot is 360m.

b) Calculate the area of that garden plot.

c) In the middle of the garden, a square fish pond with a perimeter of 100m is dug. Calculate the remaining area for cultivation.

Question 5: A triangular piece of land has one perpendicular side measuring 44m and equals 4/3 of the other perpendicular side. A square flower bed with a perimeter of 12m is built on this piece of land. Calculate the remaining area of the land.

Question 6: A triangular piece of land has an area twice that of a square with a side length of 60m. The height is 180m. Calculate the base length of the land?

Question 7: A right-angled triangle has a total of the two perpendicular sides measuring 88m and this perpendicular side is 0.6 times the length of the other perpendicular side. On this farmland, rice is planted, yielding 70kg of rice per 100m² on average. How many kilograms of rice are harvested on the entire farmland?

Question 8: A triangular flower bed with a base length of 6m and a height of 3.5m is built in the middle of a square yard with a perimeter of 64m. Calculate the remaining area of the yard after building the flower bed?

Question 9: A triangle drawn to scale has an area of 30dm². Calculate the base length of the triangle knowing its actual height is 36m.

Question 10: A triangle has an area three times that of a rectangle with a length of 42 dm and a width of 24dm. Calculate the height of the triangle, knowing the base length of the triangle is 96dm.

Question 11: A triangle with a base of 0.8cm. The height is 7/4 times the base. Calculate the area of the triangle.

Question 12: A square plot of land has a side length of 18m and a triangular plot of land has a height of 12m. It is known that the two plots of land have the same area. Calculate the base length of the triangular plot of land.

Question 13: A rectangular plot of land has a length of 24m and is 6m wider. In the middle of the plot, a triangular flower bed with a height of 7.5m and equals 3/5 of the base length is built. Calculate:

a) Area of the flower bed.

b) Area of the remaining plot of land.

Question 14: A triangular garden plot has a base equal to 3/5 of the height and the difference in height is 40m.

a) Calculate the area of that garden plot.

b) All 156 trees planted in the garden are either orange or lemon trees, with 18 more orange trees than lemon trees. Calculate the number of each type of tree planted in the garden.

Question 15: A triangular plot of land has a long base side of 180m and an area equal to the area of a square with a perimeter of 240m. Calculate the height of the triangular plot of land.

Question 16: A triangle has a base side of 20m and an area equal to the area of a rectangle with a length of 16.5m and a width of 8m. Calculate the height of the triangle.

Question 17: Given right triangle ABC with perimeter 237.6cm. Side AB is 19.8dm longer than side AC. Side BC measures 99dm. Calculate the area of right triangle ABC?

Question 18: A rectangular yard has a perimeter of 50m, with the length exceeding the width by 10m. A triangular pond with a base side of 5.2m and a height of 4.9m is dug in the yard. Calculate the remaining area of land.

Question 19: A triangle has an area of 120cm². If the base is extended by 3cm, the area will increase by 30cm². Calculate the base length of the triangle.

Question 20: A triangle has a base of 20.5m. If the base is reduced by 4.7m, the area will decrease by 35.72m². Calculate the original area of the triangle?

Question 21: A triangular plot of land has a difference between the base and the height of 10.5m. Calculate the area of the plot of land, knowing that if the base length is increased by 3.6m, the area will increase by 79.2m².

Question 22: A triangular garden plot has vertex A and base BC measuring 45m. If the base BC is extended by a segment CD measuring 15m, the area will increase by 225m².

a) Calculate the area of the garden plot in hectares.

b) Vegetables are grown on the garden plot, yielding 35.6kg of vegetables for every 300m². Calculate the weight of vegetables harvested from the garden plot.

Question 23: A triangular plot of land with a right angle has a total of 88m for the two perpendicular sides. If one perpendicular side is extended by 3.4m, the area will increase by 66.3m². Calculate the measurement of the remaining perpendicular side.

Question 24: A triangle has a total of 30.5cm for the base and height. If the base is reduced by 2.3cm, the area will decrease by 13.8cm². Calculate the original area of the triangle?

Question 25: A triangular field has an area of 810m². If the base is reduced by 3.6m, the area will decrease by 64.8m².

a) Calculate the original base length of the field.

b) On average, for every 50m² of land, farmers harvest 32.5kg of rice. Calculate the total weight of rice harvested from the entire field in tons?

More: Advanced Grade 5 trapezoid problems with answers

Through these Grade 5 triangle problems, students quickly grasp how to identify shapes, calculate the perimeter and area of triangles, thereby effectively solving any Grade 5 triangle-related problems. Additionally, this is a useful resource for teachers to easily collect Grade 5 triangle problem types for triangle topics.

Frequently Asked Questions

What are some important triangle problems for grade 5 students to study?

Grade 5 students should focus on understanding both basic and advanced triangle problems, including calculations of area and perimeter, as these concepts frequently appear in tests and exams.

How can students effectively learn to solve triangle problems in mathematics?

Students can enhance their problem-solving skills by practicing a variety of triangle problems, comparing their solutions with provided answers, and referring to theoretical concepts related to triangle mathematics.

What formulas are essential for calculating the area of triangles in grade 5?

The primary formula for calculating the area of a triangle is Area = 1/2 × base × height. Students should be familiar with this formula and its application in different problems.

What are the types of triangle exercises included in grade 5 textbooks?

Grade 5 textbooks typically include exercises on calculating the area of triangles, identifying triangle angles and sides, and comparing areas of different triangles, providing a comprehensive understanding of triangle geometry.

Why is it necessary for grade 5 students to study triangle mathematics?

Studying triangle mathematics is essential for grade 5 students because it reinforces their understanding of geometric concepts and prepares them for more advanced mathematical topics in future grades.

What challenges do students face when solving advanced triangle problems?

Students often encounter challenges such as understanding complex problem statements, applying multiple formulas correctly, and visualizing triangle dimensions, which requires practice and guidance to overcome.

How do triangle problems appear in grade 5 mathematics exams?

Triangle problems frequently appear in grade 5 mathematics exams in various forms, including direct calculations of area and perimeter, comparisons of triangles, and applied problems that require critical thinking.

What resources can assist grade 5 students in mastering triangle concepts?

Students can benefit from textbooks, exercise books, online resources, and tutoring that provide clear explanations, diverse problem sets, and step-by-step solutions to enhance their understanding of triangle concepts.

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