Let’s use some old exam question to practice finding the area of composite shapes. The difficulty increases as we go down the page.

Question set 1:

(1a.)

(1b.)

(1c.)

Question set 2:

(2a.)

(2b.)

(2c.)

(2d.)

(2e.)

(2f.)

(2g.)

(2h.)

Question set 3:

(3a.)

What is the area of the shaded region in the rectangle below?:

(3b.)

Three-quarters of the area of the rectangle below has been shaded. What is the value of x?

(3c.) In terms of a, b and c, what is the area of the pentagon shown below:

(3d.) Two rectangles of dimensions 8 cm by 10 cm and 9 cm by 12 cm overlap as shown in the diagram below. The area of the black region is 37 cm². What is the area of the grey region?

(3e.) Calculate the value of x in the diagram below:

Answers

(1a.) 16cm², (1b.) 7cm², (1c.) 12cm²;

(2a.) 39cm², (2b.) 54cm², (2c.) 88cm², (2d.) 46cm² , (2e.) 111cm² , (2f.) 42cm², (2g.) 100cm², (2h.) 306cm²;

(3a.) 21cm², (3b.) x=4, (3c.) b/2(a+c), (3d.) 65cm², (3e.) 4cm