Question

find the total area of the given figure

Answer 1

Answer:

$A=996\ in^2$

Step-by-step explanation:

we know that

The total area of the figure is equal to the area of the square plus the area of the triangle

step 1

Find the area of triangle

The area of triangle is equal to

$A=\frac{1}{2}(b)(h)$

where

b is the base of triangle (is the same that the length side of the square)

h is the height of triangle

we have

$h=35\ in$

Applying the Pythagorean Theorem

Find the length side b

$37^2=35^2+(b/2)^2$

$(b/2)^2=37^2-35^2$

$(b/2)^2=144$

$(b/2)=12\\b=24\ in$

Area of triangle

$A=\frac{1}{2}(24)(35)=420\ in^2$

step 2

Find the area of the square

The area of the square is

$A=b^2$

we have

$b=24\ in$

substitute

$A=(24)^2=576\ in^2$

step 3

Find the total area of the figure

Adds the areas

$A=420+576=996\ in^2$