FINDING THE AREA OF A TRAPEZOID

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.

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.