FINDING THE AREA OF A TRAPEZOID

Find the area of each figure. Round to the nearest tenth if necessary.

Problem 1 :

Solution :

Area of trapezoid = (a + b)/2 × h

= (9 + 12)/2 × 10

= (21/2) × 10

= 105 cm²

So, the area of trapezoid is 105 cm².

Problem 2 :

Solution :

Area of trapezoid = (a + b)/2 × h

= (3 + 1.5)/2 × 2

= (4.5/2) × 2

= 4.5 ft²

So, the area of trapezoid is 4.5 ft².

Problem 3 :

Solution :

Area of trapezoid = (a + b)/2 × h

= (18 + 12)/2 × 10

= (30/2) × 10

= 150 mm²

So, the area of trapezoid is 150 mm².

Problem 4 :

Solution :

Area of trapezoid = (a + b)/2 × h

= (6.5 + 3)/2 × 4

= (9.5/2) × 4

= 19 ft²

So, the area of trapezoid is 19 ft².

Problem 5 :

Solution :

Area of trapezoid = (a + b)/2 × h

= (2 + 9.2)/2 × 7

= (11.2/2) × 7

= 39.2 cm²

So, the area of trapezoid is 39 cm².

Problem 6 :

Solution :

Area of trapezoid = (a + b)/2 × h

= (24 + 8)/2 × 20.7

= (32/2) × 20.7

= 331.2 mm²

So, the area of trapezoid is 331 mm².

Problem 7 :

Solution :

Area of trapezoid = (a + b)/2 × h

= (25 + 20.1)/2 × 12

= (45.1/2) × 12

= 270.6 ft²

So, the area of trapezoid is 271 ft².

Problem 8 :

Solution :

Area of trapezoid = (a + b)/2 × h

= (5.6 + 3.2)/2 × 6.9

= (8.8/2) × 6.9

= 30.36 in²

So, Area of trapezoid is 30.4 in².

Problem 9 :

Trapezoid: bases 22.8 mm and 19.7 mm, height 36mm

Solution :

Area of trapezoid = (a + b)/2 × h

= (22.8 + 19.7)/2 × 36

= (42.5/2) × 36

= 765 mm²

So, Area of trapezoid is 765 mm².

Problem 10 :

Trapezoid: bases 5 ft and 3.5 ft, height 7 ft

Solution:

Area of trapezoid = (a + b)/2 × h

= (5 + 3.5)/2 × 7

= (8.5/2) × 7

= 29.75 ft²

So, Area of trapezoid is 30 ft².

Problem 11 :

Find x for each trapezium.

Solution:

Area of trapezium = 36 cm²

(1/2) x h x (a + b) = 36

a = 8, b = x and h = 4

(1/2) x 4 x (8 + x) = 36

2(8 + x) = 36

8 + x = 36/2

8 + x = 18

x = 18 - 8

x = 10 cm 

So, the missing side is 10 cm.

Problem 12 :

Solution:

Area of trapezium = 55 cm²

(1/2) x h x (a + b) = 55

a = 9, b = x and h = 5

(1/2) x 5 x (9 + x) = 55

(1/2)(9 + x) = 55/5

9 + x = 11(2)

9 + x = 22

x = 22 - 9

x = 13

So, the missing side is 13 cm.

Problem 13 :

Solution:

Area of trapezium = 55 cm²

(1/2) x h x (a + b) = 55

a = 9, b = x and h = 5

(1/2) x 5 x (9 + x) = 55

(1/2)(9 + x) = 55/5

9 + x = 11(2)

9 + x = 22

x = 22 - 9

x = 13

So, the missing side is 13 cm.

Problem 14 :

Mr Taylor keeps chickens in the field shown. Each chicken needs 3m². What is the maximum number of chickens he can keep in the field?

Solution :

Height = 18 m, length of parallel sides a = 24 m and b = 10 m

Area of trapezium = (1/2) x h (a + b)

= (1/2) x 18 x (24 + 10)

= 9 x 34

= 306 square meter

So, the required area of trapezium is 306 square meter.

Problem 15 :

The trapezium and the triangle have the same area. Calculate the height of the triangle

Solution:

Area of trapezium = area of triangle

(1/2) x h (a + b) = (1/2) x base x height

Height of trapezium = 8 cm, parallel sides a= 23 cm and b = 7 cm

Base of the triangle = 12 cm and height = h cm

1/2 x 8 x (23 + 7) = (1/2) x 12 x h

4 x 30 = 6h

h = 120/6

h = 20 cm

So, the required height of the triangle is 20 cm.