Question

A garden is in the shape of a square with a semicircle on one of its sides. The side of the square is $7$ m. What is the area of the garden in sq. m.?

• A. $68\frac{1}{4}$
• B. $49$
• C. $58\frac{5}{8}$
• D. $70$

Answer 1

The correct option is A $68\frac{1}{4}$

The side of the square is $7m$.

Hence, the area of the square part of the garden $=7^2=49$ sq. m.

The semicircle lies on one of the sides of the square part of the garden.

So, its radius $=\frac{7}{2}=3.5m$

Area of the semi-circular part of garden $=\frac{1}{2}\times \pi r^2$

$=\frac{1}{2}\times \frac{22}{7}\times \frac{7}{2}\times \frac{7}{2}=\frac{77}{4}$ sq. m.

Area of garden $=49+\frac{77}{4}=68\frac{1}{4}$ sq. m