Question

Find the area of the $△$AEF if EF = 1 m.

• A. $1m^2$
• B. $2m^2$
• C. $\sqrt{2}{m}^2$
• D. $4m^2$

Answer 1

The correct option is A

$1m^2$

To find the Area of $△$ AEF we need to find AE.

We have : AB = BC = CD = DE = EF = 1 m

To find AE, we need to find AC, and then AD using Pythagoras theorem.

AC = $\sqrt{1^2+1^2}$ = $\sqrt{2}$ m

AD = $\sqrt{1^2+(\sqrt{2}{)}^2}$ = $\sqrt{1+2}$ = $\sqrt{3}$ m

$\therefore$ AE = $\sqrt{1^2+(\sqrt{3}{)}^2}$ = $\sqrt{1+3}$ = 2 m

Hence, Area of $△$ AEF = $\frac{1}{2}\times Base\times Height$ (Base = EF and Height = AE)

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

= $1m^2$