Question

The figure is made up of a square and a rectangle. Find the area of the unshaded region.

• A. 40 sq m
• B. 48 sq m
• C. 52 sq m
• D. 42 sq m

Answer 1

The correct option is C 52 sq m


Side length of the square ABCD = 7 m
Area of the square = Side $\times$ Side = 7 $\times$ 7 = 49 sq m
Length of the rectangle GFED, DE = CE – CD
= 16 m – 7 m = 9 m
Width of the rectangle EF = 3 m
Area of the rectangle = Length $\times$ Width = 9 m $\times$ 3 m = 27 sq m
Base of Triangle 1, DG = 3 m
Height of Triangle 1, AC = 7 m
Area of Triangle $1=\frac{1}{2}\times Base\times Height$
$=\frac{1}{2}\times 3m\times 7m$
$=10.5sqm$

Base of Triangle 2, DG = 3 m
Height of Triangle 2, DE = 9 m
Area of Triangle $2=\frac{1}{2}\times Base\times Height$
$=\frac{1}{2}\times 3m\times 9m$
$=13.5sqm$

Area of the unshaded region = Area of the square + Area of the rectangle – Area of Triangle 1– Area of Triangle 2
= 49 sq m + 27 sq m – 10.5 sq m – 13.5 sq m
= 52 sq m