Question

The figure shows four smaller squares in the corners of a large square. the smaller squares have sides of length 1cm, 2cm, 3cm and 4cm in anticlockwise order and the sides of the large square have length of 11cm.

What is the area of the shaded quadrilateral? (see attachment)

Answer 1

B. 36
`cm^(2)`

Explanation:

The shaded quadrilateral has a shape of a trapezium.

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

where: a is the side length parallel to the base, b is the base and h is the height.

The height of the figure = 11 - (4 + 1)

= 11 - 5

= 6

The height of the figure is 6 cm.

The length of its base = 11 - (1 + 2)

= 11 - 3

= 8

The length of its base is 8 cm.

The length of the side parallel to base = 11 - (4 + 3)

= 11 - 7

= 4

The parallel side length to base is 4 cm.

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

=
`(1)/(2)`(4 + 8)6

= 12 x 3

= 36

Area of quadrilateral = 36
`cm^(2)`