Question

In the figure given below, AB is the diameter of the circle and CD is the height of $△ACB.$ If the circumference of the circle is 44 cm, then what is area of $△ACB$ given that CD = 5 cm (Use $\pi =\frac{22}{7}$).

• A. $35{\text{cm}}^2$
• B. $70{\text{cm}}^2$
• C. $140{\text{cm}}^2$
• D. $220{\text{cm}}^2$

Answer 1

The correct option is A $35{\text{cm}}^2$

Circumference of a circle = $\pi \times$ diameter
$⟹$ Diameter = $\frac{Circumference}{\pi }$

$=\frac{44}{\frac{22}{7}}$

$=\frac{44\times 7}{22}=14cm$

The base of the triangle equals the diameter of the circle.
Area of a triangle =$\frac{1}{2}\times \text{base}\times \text{height}$
$\therefore \text{Area of}△ACB=\frac{1}{2}\times AB\times CD$
= $\frac{1}{2}\times 14\times 5$
= $35{\text{cm}}^2$