Question

The playground pictured here is having rubber flooring installed to help protect children against injuries from falls. If the cost, including installation, is $8.00 per square foot, what is the total cost of installing the surface?

Answer 1

$6,672

Explanation:

Area of Playground

• Area (rectangle) + 2 x Area (semicircle)
• 26 x 20 + 2 x 3.14 x 10² x 1/2
• 520 + 314
• 834 square feet

Cost

• $8.00 per square feet
• $8 x 834
• $6,672

Answer 2

Using π: $6,673.27 (nearest cent)

Using π = 3.14: $6,672

Explanation:

Separate the figure into a rectangle and two semicircles.

Area of a rectangle = width × length

= 20 ft × 26 ft

= 520 ft²

Area of a semicircle = 1/2 π r²

= 1/2 π · 10²

= 50π ft²

⇒ Total area = area of rectangle + (2 × area of semicircle)

= 520 + (2 × 50π)

= (520 + 100π) ft²

⇒ Total cost = area × cost

= (520 + 100π) × $8

= $6,673.27 (nearest cent)

**using π = 3.14**

Total cost = (520 + 100 × 3.14) × $8 = $6,672