Question

The area of the play area is 286.56 square feet. A border is planned around the perimeter of the play area. How many feet of material are needed for the border?

Answer 1

Answer: The perimeter is 68.9 ff.

Explanation:

The whole play area is 286.56 sqft. That is the rectangle plus the triangle.

We calculate the rectangle surface with 14.4 * 18.5 = 266.4 sqft.

So the triangle surface must be 286.56 - 266.4 = 20.16 sqft.

As the triangle is build around a 90-degree angle, its surface can be calculated with b * c / 2, where b is the left-hand side, c the unknown bottom side. Check it on the photo to understand, if necessary.

So (1/2) * 14.4 * c = 20.16 We don't know c, the bottom line of the triangle.

That is 7.2c = 20.16

which we device by 7.2:

c = 20.16/7.2 = 2.8

So now we have the missing bottom line of the triangle. We can now piece together the parts of the perimeter by going around with our finger and counting the lengths which we know now completely:

14.4 + 18.5 + 14.7 + 2.8 + 18.5 = 68.9 ft.

Answer 2

Explanation:

The length of material needed for the border is the perimeter of the backyard play area

How to calculate the length of material needed

The area of the play area is given as:

The area of a trapezoid is calculated using:

Where L1 and L2, are the parallel sides of the trapezoid and H represents the height.

The given parameter is not enough to solve the length of material needed.

So, we make use of the following assumed values.

Assume that the parallel sides are: 25 feet and 31 feet long, respectively.

While the other sides are 10.2 feet and 8.2 feet

The length of material needed would be the sum of the above lengths.

So, we have:

Using the assumed values, the length of material needed for the border is 74.4 feet