Solving Math for 5th Grade Page 106, Intensive Practice

Guidance on solving Math for 5th Grade Page 106 (including solving methods)

1. Solving exercise 1 - Math 5 Page 106

Problem:
Given a triangle with an area of 5/8 m² and a height of 1/2 m. Calculate the length of the base of the triangle.

Solution Method:
From the formula for calculating the area of a triangle: S = (a x h) : 2 => a = 2S : h 
=> Stating verbally: To find the length of the base of the triangle, we take twice the area of the triangle and divide it by the height. 

2. Solving exercise 2 - Solving Math for 5th Grade Intensive Practice Page 106

Solution Method:

* Students need to pay attention to the following important knowledge:
- How to calculate the area of a trapezoid: To find the area of a trapezoid, we add the large base to the small base, then multiply by the height, and divide by 2.
- How to calculate the area of a right triangle: To find the area of a right triangle, we take half the product of the two sides of the right angle.
* For the specific problem above: Observing the diagram, we see that the land is divided into a trapezoid BMCN and two triangles: ABM and CND. Therefore, we apply the above formulas, calculate the area of the shapes, and then add them together to get the area of the land.

Answer:
The area of trapezoid BMCN is:
               (38 + 20.8) x 37.4 : 2 = 1099.56 (m²)
The area of triangle ABM is:
                24.5 x 20.8 : 2 = 254.8 (m²)
The area of triangle CND is:
                25.3 x 38 : 2 = 480.7 (m²)
The area of the land is:
               1099.56 + 254.8 + 480.7 = 1835.06 (m²)
Answer: 1835.06m²

3. Solving exercise 3 - Solving Math for 5th Grade Concentrated Practice Page 106

Problem:
A rope connects two pulleys (as shown). The diameter of the pulleys is 0.35m. The two axes are 3.1m apart. Calculate the length of the rope.

Solution Method:
Students need to note: The length of the rope is equal to the sum of the lengths of two semicircles (equal to the circumference of the circle) plus 2 times the distance between the two axes.
- Step 1: Calculate the circumference of the circle with a diameter of 0.35 meters by multiplying the known diameter by the number pi (which has a value of 3.14)
- Step 2: Calculate the length of the rope by taking the circumference of the circle with a diameter of 0.35m and adding it to 2 times the distance between the two axes. 

Answer:
The circumference of the circle with a diameter of 0.35m is:
        0.35 x 3.14 = 1.099 (m)
The length of the rope is:
       1.099 + 3.1 x 2 = 7.299 (m)
                       Answer: 7.299m.

Math 5 Page 106 Solving Guide (concise)

Exercise 1 - Solving Math 5 Concentrated Practice Page 106
Given a triangle with an area of 5/8 m² and a height of 1/2m. Calculate the length of the base of the triangle.
Solution:
The length of the base of the triangle is:
Answer 1
Answer: 5/2 (m).
Remember: To find the length of the base of the triangle, we take twice the area divided by the height.

Exercise 2 Page 106 Math Textbook 5
A rectangular tablecloth has a length of 2m and a width of 1.5m. In the middle of the cloth, a diamond pattern is embroidered with diagonals equal to the length and width of the rectangle. Calculate the area of the tablecloth and the area of the diamond.
Answer 2
Solution:
The area of the tablecloth is: 2 x 1.5 = 3 (m²)
The area of the diamond is: 2 x 1.5 : 2 = 1.5 (m²)
Answer: 3m², 1.5m²