Question

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

Answer 1

Answer:

149 ft² of the garden was  covered in sod

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 $9\frac{1}{4}$ft

Area of garden = $length \times width$

Area of garden = $20 \times 9\frac{1}{4}$

Area of garden = $20 \times \frac{37}{4}$

Area of garden = $20 \times 9.25$

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 = $\frac{1}{2} \times base \times height$

On substituting the value

Area of one triangle =$\frac{1}{2} \times 6 \times 6$

Area of one triangle = $\frac{1}{2} \times 36$

Area of one triangle = $\frac{36}{2}$

Area of one triangle = $18 ft^2$

Total area of uncovered part

= $2 \times \text{area of one triangle}$

=$2\times 18$

= $36 ft^2$

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 $149 ft^2$