finding the area of trapezoids and problem solving

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Trapezoid Calculator

Trapezoid calculator

This calculator finds the unknown element of a trapezoid given any three known values. The calculator can find long and short base, side, diagonal, height, median, area perimeter and interior angle. The calculator gives you a step-by-step solution on how to find the missing value.

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finding the area of trapezoids and problem solving

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Table of Contents

Last modified on August 3rd, 2023

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Area of a trapezoid.

The area of a trapezoid is the total space enclosed by it. Since a trapezoid is a two-dimensional shape, its area also lies in a two-dimensional plane. The unit of area is in square units such as m 2 , cm 2 , in 2 , or ft 2 .

Using Height and Base Lengths

The basic formula to calculate the area of a trapezoid is given below:

Let us solve an example to understand the concept better.

As we know, Area (A) = ½ (a + b) × h, here a = 14 cm, b = 9 cm, and h = 5 cm ∴A = ½ (14 + 9) × 5 = 57.5 cm 2

Without Height

We can calculate the area of a trapezoid when all 4 sides are known. There is no definite formula as such for such a circumstance. We try to calculate the area of the triangle as a portion formed in a trapezoid and then calculate the whole area of the trapezoid.

Problem: Finding the area of a trapezoid when the SIDES are known.

Let us label the trapezoid ABCD and mark the triangles Δ1 and Δ2, formed by 2 perpendiculars drawn in. As we know, Long base is 30 cm, ∴BE + FC = long base – short base = 30 – 20 = 10 cm Δ1 and Δ2 together forms a scalene triangle (3 unequal side lengths). Here, we will use the Heron’s Formula to find the area of Δ1 and Δ2 together so as to find the perpendicular height of the trapezoid. Area of Δ1 and Δ2 ${ =\sqrt{s\left( s-a\right) \left( s-b\right) \left( s-c\right) } }$ , here s = ½(a + b + c) ∴s = ½(a + b + c), here a = 10 cm, b = 12 cm, c = 16 cm s = ½(10 + 12 + 16) = 19 cm Now, Area of Δ1 and Δ2 ${ =\sqrt{s\left( s-a\right) \left( s-b\right) \left( s-c\right) } }$ , here s = 19 cm = √[19(19 – 10)(19 – 12)( 19 – 16)] = 59.92 cm 2 Height (h) of a scalene triangle = 2A/b, here A = area, b = base ∴h = 2A/b, here A = 59.92 cm 2 , b = 10 cm ∴h = 2 × 59.92/10 = 11.984 cm Now, Area of trapezoid ABCD = ½ (a + b) × h, here a = 30 cm, b = 20 cm, h = 11.984 cm ∴A = ½ (30 + 20) × 11.984 = 299.6 cm 2