Question

Find the area of the image below:

Answer 1

Answer:

Option D. $27.7\ units^{2}$

Step-by-step explanation:

we know that

The area of the image is equal to the area of the complete square minus the area of triangle 1, minus the area of triangle 2, minus the area of triangle 3, minus the area of trapezoid 4

see the attached figure to better understand the problem

Find the area of the complete square

$A=8^{2}=64\ units^{2}$

Find the area of triangle 1

$A=(1/2)(4)(5)=10\ units^{2}$

Find the area of triangle 2

$A=(1/2)(3)(3)=4.5\ units^{2}$

Find the area of triangle 3

$A=(1/2)(3)(3)=4.5\ units^{2}$

Find the area of triangle 4

$A=(1/2)(3+4)(5)=17.5\ units^{2}$

The area of the image is equal to

$A=64-10-4.5-4.5-17.5=27.7\ units^{2}$