Question

The geometric figure is shown consists of square and $4$ semicircles. The diameters of the semicircles are the sides of the square and each diameter is $10$ centimeters long.

Calculate the approximate area of the geometric figure.

• A. $100c{m}^2$
• B. $162.8c{m}^2$
• C. $257.14c{m}^2$
• D. $206.89c{m}^2$
• E. $198c{m}^2$

Answer 1

The correct option is C $257.14c{m}^2$

Given: Diameter of the circle: $10$ cm

radius of the circle$=\frac{10}{2}=5cm$

$\because$ Diameter of the circle = Side of the square

Side of the square $=10cm$

Area of the square $={10}^{2}c{m}^2=100c{m}^2$

Area of each semicircle $=\frac{\pi r^2}{2}$

$=\frac{\pi (5{)}^2}{2}$

Area of $4$ semicircles $=\frac{\pi (5{)}^2}{2}\times 4$

$=\frac{22}{7}\times 25\times \frac{1}{2}\times 4$

$=\frac{550}{7}\times 2=157.14c{m}^2$

$\therefore$ Area of the figure = Area of the square + area of $4$ semicircles

$=100+157.14=257.14c{m}^2$