Question

Determine the area of each of the following figures. Assume that all angles that

look like right angles are right angles.​

Answer 1

Part a) The area of the figure is
`31\ ft^2`

Part b) The area of the figure is
`46\ ft^2`

Explanation:

Part a) we know that

The area of the figure is equal to the area of rectangle plus the area of trapezoid

step 1

The area of rectangle is

`A_1=(b)(h)`

we have

`b=8\ ft\\h=2\ ft`

substitute the given values

`A_1=(8)(2)=16\ ft^2`

step 2

The area of trapezoid is

`A=(1)/(2)(b_1+b_2)(h)`

we have

`b_1=4\ ft\\b_2=8-(1+1)=6\ ft\\h=3\ ft`

substitute

`A=(1)/(2)(4+6)(3)`

`A_2=15\ ft^2`

step 3

Find the area of the figure

`A=A_1+A_2`

substitute

`A=16+15=31\ ft^2`

Part b) we know that

The area of the figure is equal to the area of rectangle plus the area of two triangles

step 1

The area of rectangle is

`A_1=(b)(h)`

substitute the given values

`A_1=(5)(6)=30\ ft^2`

step 2

The area of triangle at the top is

`A_2=(1)/(2)(b)(h)`

we have

`b=4\ ft\\h=6\ ft`

substitute

`A_2=(1)/(2)(4)(6)`

`A_2=12\ ft^2`

step 3

The area of triangle at right is

`A_3=(1)/(2)(b)(h)`

we have

`b=4\ ft\\h=2\ ft`

substitute

`A_3=(1)/(2)(4)(2)`

`A_3=4\ ft^2`

step 4

Find the area of the figure

`A=A_1+A_2+A_3`

substitute

`A=30+12+4=46\ ft^2`