Area of The

Trapezoid

Trapezoid

It is a quadrilateral with exactly one pair of parallel

sides.

IllustrationBase 1

Base 2

leg leg

height height

A= ½ (b1+b2)h

h

b¹

b²

A1

A2h

Trapezoid Area Theorem

The area of any trapezoid is equal to one-half the product of the height and the

sum of the bases (b1+b2).

How to find the bases?

b1= 2A/h –b2

b2= 2A/h –b1

How to find the height?

h= 2A/b1+b2

Example:

Find the Area of trapezoid DPRS. 18 cm

Solution:A= ½(b1+b2)h =1/2 (18cm+30cm)(12cm) =288cm² 30 cm

12 cm

D

P R

S

Example:

• Find the height of the trapezoid if its area is 16cm², b1= 4cm and b2=2.4cm.

Solution:h= 2A/b1+b2 = 2(16cm²)/ 4cm+2.4cm =32cm²/6.2cm =5cm

Example:

• The bases of a trapezoid are 2 and 4 times the height. The area is 108cm². Find the height and the bases of the trapezoid.

Solution:

h= 2A/b1+b2 =2(108cm²)/ 2h+4h =216cm²/ 6hh(6h)= 216cm²6h² = 216cm²h² =36h= 6

b1= 2h = 2(6) =12

b2= 4h =4(6)

=24

Check:A=1/2(b1+b2)h108cm²=

½(12+24)6cm108cm²= ½(36)6cm108cm² = 216cm²/2108cm² = 108cm² check

Daisy Mae A. Valeroso