Question

Find the total area of the given figure

Answer 1

`A=996\ in^2`

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=(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=(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`