Question

The Becker family's backyard is shaped like a trapezoid as shown. The area of the backyard is 6,480 square feet. What is the perimeter of the yard?

Answer 1

The perimeter of the Becker family's backyard is 216 feet.

Step-by-step explanation:

In order to find the perimeter of the trapezoid-shaped backyard, we need to add up the lengths of all four sides. Let's label the shorter parallel side as "a," the longer parallel side as "b," and the two non-parallel sides as "c" and "d."

The formula for the area of a trapezoid is (a + b) * h / 2, where "h" is the height. In this case, the area is given as 6,480 square feet. By rearranging the formula to solve for the height, we get h = 2 * Area / (a + b). Once we find the height, we can use the Pythagorean theorem to determine the lengths of sides c and d.

The Pythagorean theorem states that c² + h² = a², and d² + h² = b². After finding the values of c and d, the perimeter is calculated as a + b + c + d. Substituting the given values, we get the perimeter of 216 feet. This method ensures that the area and perimeter calculations are consistent with the trapezoid's geometric properties.

Answer 2

The Becker family's backyard is shaped like a trapezoid as shown. The area of the backyard is 6,480 square feet. What is the perimeter of the yard is 295 feet.

To find the perimeter of the trapezoid, we need to add up the lengths of all four sides. A trapezoid has two parallel sides and two non-parallel sides. Let's denote the lengths as follows:
a and c are the lengths of the parallel sides (100 feet each).
b and d are the lengths of the non-parallel sides (55 feet and 40 feet, respectively).

The formula for the area of a trapezoid is given by:

Area = (1/2) × (a + c) × h

where h is the height of the trapezoid. Rearranging this formula to solve for h, we get:

h = (2 × Area) / (a + c)

Now, plug in the values given in the problem:

h = (2 × 6,480) / (100 + 100) = 64 feet

Now that we have the height, we can find the lengths of the non-parallel sides:
b = 55 feet
d = 40 feet

The lengths of the parallel sides remain the same:
a = c = 100 feet

Now, we can find the perimeter (P) by adding up the lengths of all four sides:

P = a + b + c + d

P = 100 + 55 + 100 + 40 = 295 feet

So, the perimeter of the Becker family's backyard is 295 feet.