Question

In the diagram Shown a 2 foot wide flower border surrounds the heart shaped pond.What is the area of the border?

Answer 1

This figure is what we would call a composite figure. A composite figure is a shape that is made up of multiple other shapes. when looking at the pond and the border that surrounds it, we can see that this heart shape is made up of two semi circles and a square. To find the area of the border, we will use the area formulas for semi circles and for squares:

Semi Circle Area Formula:
`\pi r^(2)` ÷ 2
Square Area Formula: length x width

Pi = 3.14
Radius = Half of the diameter, in this case 6

After finding the area of each shape, we can subtract the 2 ft width to find the area of the flower bed border.

Answer 2

Area of the border is 142.80 ft²

Explanation:

The given figure consist of three figures = 2× semicircles + 1 square.

We will calculate area of the figure including border

Area of one semicircle = (1/2)π×r²= (1/2)×π×(12/2)² = (1/2)π×(6)² = 18π ft²

Area of square = side² = 12² = 144 ft²

Total area = 144 + 18π + 18π = (144 + 36π) ft²

Now we will calculate area without border.

Area of the semicircle = (1/2)π×r² =(1/2)π×[(12-4)/2]²=(1/2)π×(4)² = 8π ft²

area of square = side²= (12-4)²= 8² = 64 ft²

Total area = 64 + 8π + 8π = (64 + 16π) ft²

Now the area of the border = Area with border - Area without border

= (144 + 36π) - (64 + 16π) = 20π + (144 - 64) = 20π + 80

= 20×3.14 + 80 = 142.80 ft²

Area of the border = 142.80 ft²