Question

How can you use the formula for area of a

parallelogram to determine the area of a trapezoid if you forgot the
formula for area of a trapezoid.

Answer 1

To find the area of a trapezoid using the parallelogram formula, imagine transforming the trapezoid into a parallelogram by extending a side. Then, calculate the area of the parallelogram and subtract the area of the extra triangle that was created in the process.

Step-by-step explanation:

To determine the area of a trapezoid using the area of a parallelogram formula, you could consider dividing a trapezoid into two parts, creating a parallelogram and a triangle. The formula for the area of a parallelogram is base times height (b × h). In the case of a trapezoid, imagine extending one of the non-parallel sides until you have a parallelogram.

For example, suppose you have a trapezoid with two parallel sides of different lengths (a and b) and a height (h). You extend one side to form a parallelogram with a base equivalent to the longer base of the trapezoid, and then subtract the area of the extra triangle you introduced. The remaining area corresponds to the trapezoid. The area of a parallelogram is just the base multiplied by the height (A = b × h), and you can use the formula for the area of a triangle, which is 1/2 × base × height, to subtract the extra area.

Answer 2

Step-by-step explanation:

The area of a parallelogram of width W and length L is A = W*L.

The area of a trapezoid of width W and different side lengths L1 and L2 is

A = W(L1 + L2)/2.

To find the area of the trapezoid, take the average of the lengths L1 and L2 of the two parallel sides and call the result L. Then apply the formula for the area of a parallelogram, given above).