Explain how the formula for the area of a trapezoid can be used to find the formulas for the areas of parallelograms and triangles?

1 Answer
Nov 30, 2015

Trapezoid has bases #a# and #b#, and the altitude #h#.
Its area is #(a+b)/2*h#.
Parallelogram: #a=b#, #=># area is #(a+a)/2*h=a*h#
Triangle: #b=0#, #=># area is #1/2*a*h#.

Explanation:

Consider a trapezoid with bases #a# and #b# and an altitude #h#.

If #a=b#, trapezoid becomes a parallelogram because any quadrilateral with two opposite side congruent and parallel to each other is parallelogram.
So, the area of parallelogram can be obtained using a formula for an area of parallelogram, taking into consideration #a=b#, which result in
#S_p = (a+a)/2*h=a*h#

If #b=0#, trapezoid becomes a triangle because of side will have zero length and quadrilateral turns into triangle.
So, the area of triangle can be obtained using a formula for an area of parallelogram, taking into consideration #b=0#, which result in
#S_t = a/2*h=1/2*a*h#