How many square feet of outdoor carpet will
we need for this hole?

Number of square feet of carpet needed is 38ft²

Step-by-step explanation:

Given

A hole formed by a rectangle and a triangle.

The dimension of the rectangle is as follows:

Width = 8 ft

Length = 3 ft

The dimension of the triangle is as follows:

Base = 7 ft

Height = 4 ft

Required:

The area of the hole

First, how did we derive the dimension of the triangle?

From the diagram above;

One will observe that the length of the rectangle (12ft) extends to the top of the triangle

The distance between the top of the triangle and the bottom is calculated by 12ft - 8ft

This gives the height of the triangle

So, height = 4ft

Similarly, the base of the triangle extends to the top of the rectangle.

The region is formed by the adding the length of the rectangle to 3ft as it is in the given figure

The actual base of the triangle = 3ft + 4ft

Base = 7ft.

See attachment for detailed representation of the given diagram

Now, the area of the carpet can be calculated.

The area of the carpet is equivalent to the area of the hole.

The area of the hole is calculated by:

Area of the triangle + Area of the rectangle.

First, let's calculate the area of the triangle

Area = ½ base * height

Area = ½ * 7 ft * 4 ft

Area = ½ * 28ft²

Area = 14ft²

Area of the rectangle is calculated as follows

Area = length * width

Area = 8 ft * 3 ft

Area = 24ft²

Hence, the area of the hole = 14ft² + 24ft²

Area of the hole = 38ft²

9 x 8 divided by (5-3)=36