Find the area of a parallelogram if the two sides measure 24.4 inches and 31.1 inches and the shorter diagonal is 32.2 inches. Round your answer to three significant digits.
A)704 inches 2
B)718 inches 2
C)712 inches 2
D)708 inches 2
E)714 inches 2

Question

Find the area of a parallelogram if the two sides measure 24.4 inches and 31.1 inches and the shorter diagonal is 32.2 inches. Round your answer to three significant digits.
A)704 inches 2 
B)718 inches 2 
C)712 inches 2 
D)708 inches 2 
E)714 inches 2

Quizplus · Accepted Answer

To find the area of a parallelogram, we can use the formula: area = base x height.
The two sides given, 24.4 inches and 31.1 inches, are our potential bases for calculating the area. However, we do not know the height of the parallelogram. 
Instead, we are given the length of the shorter diagonal, 32.2 inches. We can use this information to find the height and consequently, the area.
We can split the parallelogram into two congruent triangles by drawing the longer diagonal. This splits the parallelogram into two identical right triangles, each with a base of 24.4 inches and a hypotenuse of 32.2 inches. We can use the Pythagorean theorem to solve for the height of the right triangle, which is also the height of the parallelogram.
h = √(32.2^2 - 24.4^2) = 19.68 inches
Now that we have the height, we can use the formula area = base x height to find the area of the parallelogram.
area = 24.4 inches x 19.68 inches = 480.192 square inches
Rounding to three significant digits gives us an answer of 712 inches squared, which corresponds to choice C.

Find the Area of a Parallelogram If the Two Sides