Question

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

Answer 1

Area = 26ft²

Explanation:

To solve this problem, we'll have to break the "hole" into its respective shapes so as to make it easy to solve.

In the hole, we have 1 rectangle and two triangles of different dimensions.

1. Rectangle

Area of a rectangle = length * width

Length of the rectangle = 8ft

Width of the rectangle = 3 ft

Area of the rectangle = 8 * 3 = 24ft²

2. Triangle

Area of the triangle = ½(b * h)

b = breadth of the triangle

H = height of the triangle

But since both triangle have the same height, we can calculate of one and use the value for the second one.

Height of the triangle = length of the hole - length of the rectangle

Height of the triangle = 12 - 8 = 4ft

For the first triangle,

The breadth of the triangle is 4 ft

Area of the triangle = ½ ( b * h)

Area = ½ *( 4 * 4)

Area = ½ * 16 = 8ft²

3. Area of the third triangle = ½ (b * h)

Breadth of the second triangle = 3ft

Height of the triangle = 4ft

Area = ½ (4 * 3) = ½ * 12 = 6ft²

Total area of the hole = area of rectangle + area of first triangle + area of second triangle

Total area of the hole = (12 + 8 + 6)ft² = 26ft²

Answer 2

Number of square feet of carpet needed is 38ft²

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