What is the area of the shaded region

Question

asked Nov 14, 2020 156k views

2 Answers

Emurad · Answer 1 · 2020-11-19T00:50:32+0000

For this case we must find the area of the octagon and subtract the area from the square, in order to obtain the area of the shaded region.

$A_ {sr} = A_ {oc} -A_ {sq}$

So:

$A_ {oc} = \frac {P * a} {2}$

Where:

P: It is the perimeter

a: It is the apothem

We have to:

$P = 8 * 13 = 104\\a = 15.69$

Substituting:

$A_ {oc} = \frac {104 * 15.69} {2}\\A_ {oc} = 815.88 \ square \ units$

On the other hand:

$A_ {sq} = 13 * 13\\A_ {sq} = 169 \ square \ units$

Finally:

$A_ {sr} = 815.88 \ square \ units \ -169 \ square \ units\\A_ {sr} = 646.88 \ square \ units$

Answer:

Option A