Question

A garden is sodded in the shaded portion below. How many square feet were covered with sod

Answer 1

149 ft² of the garden was covered in sod

Step-by-step explanation:

The area covered with sod = total area of the rectangle - area of the both the triangles

Step 1: Finding the total area of the rectangle

The garden is rectangular shape

It's dimensions are 20 ft and
`9(1)/(4)`ft

Area of garden =
`length * width`

Area of garden =
`20 * 9(1)/(4)`

Area of garden =
`20 * (37)/(4)`

Area of garden =
`20 * 9.25`

Area of garden =
`185 ft^2`

Step 2: Finding the areas of the two triangles:

The two triangles are congruent.Hence its enough to find the area of one triangle

The base and height of the triangle is 6 ft

Area of one triangle =
`(1)/(2) * base * height`

On substituting the value

Area of one triangle =
`(1)/(2) * 6 * 6`

Area of one triangle =
`(1)/(2) * 36`

Area of one triangle =
`(36)/(2)`

Area of one triangle =
`18 ft^2`

Total area of uncovered part

=
`2 * \text{area of one triangle}`

=
`2* 18`

=
`36 ft^2`

Step 3: Finding the area covered with sod

The area covered with sod = area of the rectangle - area of the of uncovered part

The area covered with sod = 185 - 36 = 149

The area covered with sod
`149 ft^2`