PROBLEMS ON FINDING AREA OF TRAPEZIUM

A trapezoid is also known as a trapezium is a four-sided polygon or a quadrilateral. It has one set of opposite sides which are parallel and a set of non-parallel sides.

The parallel sides are known as the bases and the non-parallel sides are known as the legs of the trapezoid.

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

Here a and b area parallel sides and h is height.

Perimeter of the trapezoid = Sum of length of all sides.

Problem 1 :

A trapezoid has an area of 60 cm² and its height is 6 cm and one base is 8 cm. What is the other base length?

Solution :

Area of trapezium = 60 cm²

height = 6 cm and base (a) = 8 cm and base (b) = ?

(1/2) x h x (a + b) = 60

(1/2) x 6 x (8 + b) = 60

3(8 + b) = 60

8 + b = 60/3

8 + b = 20

b = 20 - 8

b = 12 cm

So, the missing base is 12 cm.

Problem 2 :

If a trapezoid has an area of 65 ft² and the lengths of the bases are 12 ft and 14 ft, find the height. 

Solution :

Area of trapezium = 65 ft²

height (h) = ? and base (a) = 12 ft and base (b) = 14 ft

(1/2) x h x (a + b) = 65

(1/2) x h x (12 + 14) = 65

(1/2) x h x 36 = 65

18h = 65

h = 65/18

h = 3.61 ft

So, the missing height is 3.61 ft.

Problem 3 :

If a trapezoid has an area of 180 m² and its height is 12 m and one base is 20 m, find the other base length.

Solution :

Area of trapezium = 180 m²

height (h) = 12 m and base (a) = 20 m and base (b) = ?

(1/2) x h x (a + b) = 180

(1/2) x 12 x (20 + b) = 180

6 x (20 + b) = 180

20 + b = 180 / 6

20 + b = 30

b = 30 - 20

b = 10 m

So, the missing base is 10 m.

Problem 4 :

The area of a trapezoid is 625 ft² and its height is 25 ft. If one base of the trapezoid is 15 ft, what is the other base length?

Solution :

Area of trapezium = 625 ft²

height (h) = 25 ft and base (a) = 15 ft and base (b) = ?

(1/2) x h x (a + b) = 625

(1/2) x 25 x (15 + b) = 625

12.5 x (15 + b) = 625

15 + b = 625/12.5

15 + b = 50

b = 50 - 15

b = 35 ft

So, the missing base is 35 ft

Problem 5 :

The base lengths of a trapezoidal tabletop are 6 feet and 8 feet. The height is 5 feet. What is the area of the tabletop?

Solution :

height (h) = 5 ft and base (a) = 6 ft and base (b) = 8 ft

Area of trapezium = (1/2) x 5 x (6 + 8)

= (1/2) x 5 x 14

= 7 x 5

= 35 square feet

Problem 6 :

The Pentagon in Arlington, Virginia, is the headquarters of the U.S. Department of Defense.

a. Find the perimeter of the Pentagon.

b. A pentagon is made of a triangle and a trapezoid. The height of the triangle shown is about 541 feet, and the height of the trapezoid shown is about 876 feet. Estimate the land area of the Pentagon.

Solution :

a)

Perimeter of the pentagon = 5(921)

= 4605 ft

b) Area of pentagon = area of trapezoid + area of triangle

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

height of the trapezoid = 876 feet and height of triangle = 541 feet

= (1/2) x 876 x (921 + 1490)

= 438 x 2411

= 1056018 square feet 

Area of triangle = (1/2) x 1490 x 541

= 745 x 541

= 403045 square feet

Area of pentagon = 1056018 + 403045

= 1459063 square feet

Problem 7 :

How much material do you need to make two back pockets?

Solution :

Height of trapezoid = 9 cm, a = 12 cm and b = 20 cm 

height of triangle = 3 cm

Area of pocket = area of trapezium + area of triangle

= (1/2) x 9 x (12 + 20) + (1/2) x 10 x 3

= 4.5 x 32 + 5 x 3

= 144 + 15

= 159 cm²

Problem 8 :

In a grid of the exhibits at a zoo, the vertices of the giraffe exhibit are E (0, 90), F (60, 90), G (100, 30), and H (0, 30). The coordinates are measured in feet. What is the area of the giraffe exhibit?

Solution :

Distance between (0, 90) and (0, 30) = 60 units

height of trapezium = 60 units

Distance between (0, 90) and (60, 90) = 60 units

a = 60 units

Distance between (0, 30) and (100, 30) = 100 units

b = 100 units

Area of giraffe exhibit = (1/2) x 60 x (60 + 100)

= 30 x 160

= 4800 square units.