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Find the area of a trapezoid with bases 24 and 36 with 45 base angles

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A trapezoid with congruent base angles have the other two sides (that are not the bases) congruent to each other:

And the area A of a trapezoid with bases a and b, and height h is given by:


A=(a+b)/(2)\cdot h

Thus, we need to find the height h of this trapezoid and then use it to calculate its area.

Step 1

We can find h by using the tangent of 45º. We obtain:


\begin{gathered} (h)/(6)=\tan 45^(\circ) \\ \\ (h)/(6)=1 \\ \\ h=1\cdot6 \\ \\ h=6 \end{gathered}

Step 2

Now, we have:

a = 24

b = 36

h = 6

Thus, the area A of the trapezoid is:


\begin{gathered} A=(24+36)/(2)\cdot6 \\ \\ A=(60)/(2)\cdot6 \\ \\ A=30\cdot6 \\ \\ A=180 \end{gathered}

Find the area of a trapezoid with bases 24 and 36 with 45 base angles-example-1
User Darshan Puranik
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