Question

8ftÜ4ft7ft5ftA right angle is removed from a rectangle to create the shaded region shown below find the area of the shaded region be sure to include the correct unit in your answer

Answer 1

First, we need to find the sides of the triangle.

The base of the triangles is 8ft - 5ft = 3ft.

The height for the triangle is 7ft - 4ft = 3ft

Now, we need to find the area of the triangle:

`A_t=(base\cdot height)/(2)`

Replacing the values:

`A_t=(3ft\cdot3ft)/(2)`

Then

`A_t=4.5ft^2^{}`

Now, we need to find the area for the rectangle:

Area for a rectangle = Length * Width

In this case:

Length = 8ft

Width = 7ft

Therefore:

`A_r=8ft\cdot7ft`

Then

`A_r=56`

Finally, to find the area of the shaded region we need to subtract the triangle area from the rectangle area:

`A=A_r-A_t`

Therefore:

`A=56ft^2-4.5ft^2`
`A=51.5ft^2`

Hence, the area for the shaded region is 51.5 ft².