Question

find the area of the regular hexagon below by using the area formula for triangles. a = 11 inches and b = 14 inches. picture not drawn to scale a. 154 in² b. 462 in² c. 42 in² d. 77 in²

Explanation:

Step1: Recall triangle - area formula

The area formula for a triangle is $A_{\triangle}=\frac{1}{2}\times base\times height$.

Step2: Identify base and height for sub - triangles of hexagon

For the regular hexagon, when divided into 6 congruent triangles, the base of each triangle is $b = 14$ inches and the height is $a=11$ inches.

Step3: Calculate area of one triangle

$A_{\triangle}=\frac{1}{2}\times b\times a=\frac{1}{2}\times14\times11 = 7\times11=77$ square inches.

Step4: Calculate area of hexagon

A regular hexagon can be divided into 6 congruent triangles. So $A_{hexagon}=6\times A_{\triangle}$.
$A_{hexagon}=6\times77 = 462$ square inches.

Answer:

B. $462$ in²