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 [tex]9\frac{1}{4}[/tex]ft
Area of garden = [tex]length \times width[/tex]
Area of garden = [tex]20 \times 9\frac{1}{4}[/tex]
Area of garden = [tex]20 \times \frac{37}{4}[/tex]
Area of garden = [tex]20 \times 9.25[/tex]
Area of garden = [tex]185 ft^2[/tex]
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 = [tex]\frac{1}{2} \times base \times height[/tex]
On substituting the value
Area of one triangle =[tex]\frac{1}{2} \times 6 \times 6[/tex]
Area of one triangle = [tex]\frac{1}{2} \times 36[/tex]
Area of one triangle = [tex]\frac{36}{2}[/tex]
Area of one triangle = [tex]18 ft^2[/tex]
Total area of uncovered part
= [tex]2 \times \text{area of one triangle}[/tex]
=[tex]2\times 18[/tex]
= [tex]36 ft^2[/tex]
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 [tex]149 ft^2[/tex]
