Solving Math Problems for 5th Grade on page 127, Focusing Practice

Guidelines for solving 5th Grade Math problems on page 127 (including solving methods)

1. Solve exercise 1 - Solve Math 5 page 127

Problem: 
Given trapezoid ABCD (see diagram) with AB = 4cm, DC = 5cm, AD = 3cm. Joining D with B forms two triangles ABD and BDC.
a) Calculate the area of each triangle.
b) Calculate the percentage ratio of the area of triangle ABD to the area of triangle BDC.

Solution Method: 
Applying formulas: 
- Formula for calculating area of a general triangle: S = (a x h) : 2
=> To find the area of a general triangle, multiply the base length by the height, then divide by 2.

2. Solve exercise 2 - Solve Math 5 concentration training page 127

Problem:
Given parallelogram MNPQ (see diagram) with MN = 12cm, height KH = 6cm. Compare the area of triangle KQP with the sum of the areas of triangles MKQ and KNP.

Solution Method: 
- Problem states: Parallelogram MNPQ has MN = 12cm, height KH = 6cm
- Problem requires: Compare the area of triangle KQP with the sum of the areas of triangles MKQ and KNP
- Solution approach: 
+ Calculate the area of parallelogram MNPQ by multiplying the height by the base.
+ Calculate the area of triangle KQP by multiplying the height by the length of the base of the triangle, then divide by 2.
+ Calculate the sum of the areas of triangles MKQ and KNP by subtracting the area of triangle KQP from the area of parallelogram.

Answer:  
The area of parallelogram MNPQ is: 12 x 6 = 72 (cm²)
The area of triangle KQP is: 12 x 6 : 2 = 36 (cm²)
The sum of the areas of triangles MKQ and KNP is:
72 - 36 = 36 (cm²)
So, the area of triangle KQP is equal to the sum of the areas of triangles MKQ and KNP.

3. Solve exercise 3 - Solve Math 5 comprehensive practice page 127

Solution Method:
- Given data: The diameter of circle O is 5cm (equal to side AC of right triangle BAC at right angle B); side AB = 3cm; side BC = 4 cm.
- Problem requires: Calculate the area of the colored part of the circle
- Solution approach:
+ Step 1: Calculate the radius of the circle by dividing the diameter by 2.
+ Step 2: Calculate the area of the circle using the formula: S = r x r x 3.14 (S is the area; r is the radius).
+ Step 3: Calculate the area of right triangle BAC: S = a x b : 2 (S is the area; a, b are the lengths of the two perpendicular sides).
+ Step 4: Calculate the area of the colored part of the circle by subtracting the area of triangle BAC from the area of the circle.

Answer:
Observing the diagram we see the diameter of circle O is 5cm.
The radius of the circle is:
5 : 2 = 2.5 (cm)
Applying the formula for the area of a circle, we have the area of the circle is:
2.5 x 2.5 x 3.14 = 19.625 (cm²)
Applying the formula for the area of a triangle, we have the area of right triangle ABC is:
3 x 4 : 2 = 6 (cm²)
So, the area of the colored part of the circle is:
19.625 - 6 = 13.625 (cm²)
Answer: The area of the colored part of the circle is: 13.625cm².

Guidelines for solving Math 5 page 127, Focused training (concise)