Question #158221

The bases of an isosceles trapezoid are 12 inches and 18 inches, and the legs are 5

inches. A rectangle equal in area to the trapezoid has one dimension 6 inches.

Find the other dimension.



1
Expert's answer
2021-02-02T06:20:29-0500

Find the height of the isosceles trapezoid hh from the Pythagorean Theorem


52=h2+(18122)25^2=h^2+(\dfrac{18-12}{2})^2

Then h=4 inh=4\ in

The area of the trapezoid


At=(18+122)h=15(4)=60 in2A_t=(\dfrac{18+12}{2})h=15(4)=60\ {in}^2

The area of the rectangle


Ar=length×width=6×widthA_r=length\times width=6\times width

Given At=ArA_t=A_r


6×width=606\times width=60

width=10 inwidth=10\ in

A rectangle is equal in area to the trapezoid has another dimension of 10 inches.



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