Question

What is the area of the triangle ACD?

• A. $4c{m}^2$
• B. $2\sqrt{2}c{m}^2$
• C. $8\sqrt{2}c{m}^2$
• D. $4\sqrt{2}c{m}^2$

Answer 1

The correct option is C

$8\sqrt{2}c{m}^2$

To find the area of the triangle ACD we need to find the side AC.

AC = $\sqrt{A{B}^2+B{C}^2}$

AC = $\sqrt{4^2+4^2}$ = $\sqrt{32}$ = $4\sqrt{2}$ cm

Area $△$ACD = $\frac{1}{2}\times AC\times CD$

= $\frac{1}{2}\times 4\sqrt{2}\times 4$

= $8\sqrt{2}c{m}^2$