Chapters

## Exercise 1

Determine the area of an isosceles right triangle with the equal sides each measuring 10 cm in length.

## Exercise 2

Calculate the number of trees that can be planted in a rectangular field which is 32 m long and 30 m wide if each tree needs 4 m² to grow.

## Exercise 3

The area of a trapezoid is 120 m², the height is 8 m, and the smaller base measures 10 m. What is the length of the other base?

## Exercise 4

Calculate the area of a parallelogram whose height is 2 cm and its base is 3 times its height.

## Exercise 5

What is the area of the shaded area in the figure if the area of the entire hexagon is 96 cm²?

## Exercise 6

Calculate the area of a rhombus whose larger diagonal measures 10 cm and whose minor diagonal is half the length of the other.

## Exercise 7

Calculate the number of square tiles needed to cover a rectangular surface of 4 m by 3 m if the length of each side of the tiles is 10 cm.

## Exercise 8

The perimeter of an equilateral triangle is 0.9 dm and its height is 25.95 cm. Calculate the area of the triangle.

## Exercise 9

A rectangular field has a length of 170 m and a width of 28 m. Calculate:

1The area of the field in hectares.

2The price to re-seed the field if each square meter costs $15.

## Solution of exercise 1

Determine the area of an isosceles right triangle with the equal sides each measuring 10 cm in length.

A = (10 · 10) : 2 = 50 cm²

## Solution of exercise 2

Calculate the number of trees that can be planted in a rectangular field which is 32 m long and 30 m wide if each tree needs 4 m² to grow.

A = 32 · 30 = 960 m²

960 : 4 = 240 trees

## Solution of exercise 3

The area of a trapezoid is 120 m², the height is 8 m, and the smaller base measures 10 m. What is the length of the other base?

## Solution of exercise 4

Calculate the area of a parallelogram whose height is 2 cm and its base is 3 times its height.

h = 2 cm

b = 2 · 3 = 6 cm

A = 2 · 6 = 12 cm²

## Solution of exercise 5

What is the area of the shaded area in the figure if the area of the entire hexagon is 96 cm²?

96 : 6 = 16 cm²

16 · 2 = 32 cm²

## Solution of exercise 6

Calculate the area of a rhombus whose larger diagonal measures 10 cm and whose minor diagonal is half the length of the other.

D = 10 cm

d = 10 : 2 = 5 cm

A = (10 · 5) : 2 = 25 cm²

## Solution of exercise 7

Calculate the number of square tiles needed to cover a rectangular surface of 4 m by 3 m if the length of each side of the tiles is 10 cm.

A_{S} = 4 · 3 = 12 m² = 120,000 cm²

A_{B} = 10 · 10 = 100 cm²

120,000 : 100 = 1,200 tiles

## Solution of exercise 8

The perimeter of an equilateral triangle is 0.9 dm and its height is 25.95 cm. Calculate the area of the triangle.

P = 0.9 dm = 90 cm

l = 90 : 3 = 30 cm

A = (30 · 25.95) : 2 = 389.25 cm²

## Solution of exercise 9

A rectangular field has a length of 170 m and a width of 28 m. Calculate:

1The area of the field in hectares.

A = 170 · 28 = 4,760 m²

4,760 : 10,000 = 0. 476 ha

2The price to re-seed the field if each square meter costs $15.

4,760 · 15 = $71,400

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