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High School
Geometry
High school geometry
Analytic geometry

Irvin Dukes

Answered question

2021-12-09

Can you write the formula for the area of a trapezoid?

Answer & Explanation

servidopolisxv

Beginner2021-12-10Added 27 answers

The area of the trapezoid is the sum of the areas of the two triangles and the rectangle formed by the additional lines constructed.
The rectangle has sides of length h and

b_{1}

and the area

b_{1} h

respectively.
The triangles have areas

\frac{a_{1}}{2}

and

\frac{a_{2}}{2}

and their sum is

\frac{a_{1} + a_{2}}{2} h

But

a_{1} + b_{1} + a_{2} = b_{2} \Rightarrow a_{1} + a_{2} = b_{2} - b_{1}

Thus, the sum of the areas of triangles is

\frac{b_{2} - b_{1}}{2} h

We add this to the aarea of the rectangle to obtain the area of the trapezoid as:

A r e a = \frac{b_{1} + b_{2}}{2} h

Corgnatiui

Beginner2021-12-11Added 35 answers

A r e a = \frac{b_{1} + b_{2}}{2} h

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