# Rectangle Problems

### Solutions

1Calculate the area and perimeter of a rectangle with a base of 10 cm and a height of 6 cm.

2Calculate 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.

3Calculate the area of the quadrilateral that results from drawing lines between the midpoints of the sides of a rectangle whose base and height are 8 and 6 cm respectively.

4Calculate 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.

5A rectangular garden has dimensions of 30 m by 20 m and is divided in to 4 parts by two pathways that run perpendicular from its sides. One pathway has a width of 8 dm and the other, 7 dm. Calculate the total usable area of the garden.

6Calculate the length of the diagonal of a rectangle with a base of 10 cm and a height of 6 cm.

7A rectangular field has a length of 170 m and a width of 28 m. Calculate:

1 The area of the field in hectares.

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

## 1

Calculate the area and perimeter of a rectangle with a base of 10 cm and a height of 6 cm.

P = 2 · (10 + 6) = 32 cm

A = 10 · 6 = 60 cm^{2}

## 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

## 3

Calculate the area of the quadrilateral that results from drawing lines between the midpoints of the sides of a rectangle whose base and height are 8 and 6 cm respectively.

## 4

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 m^{2} = 120,000 cm²

A_{B} = 10 · 10 = 100 cm²

120,000 : 100 = 1,200 tiles

## 5

A rectangular garden has dimensions of 30 m by 20 m and is divided in to 4 parts by two pathways that run perpendicular from its sides. One pathway has a width of 8 dm and the other, 7 dm. Calculate the total usable area of the garden.

8 dm = 0.8 m

h = 20 - 0.8 = 19.2 m

7 dm = 0.7 m

b = 30 - 0.7 = 29.3m

A_{J} = 19.2 · 29.3 = 562.56 m²

## 6

Calculate the length of the diagonal of a rectangle with a base of 10 cm and a height of 6 cm.

## 7

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