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# What is the area of the trapezoid

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AB and CD are parallel, and AB < CD

. . Jul 29, 2020

#1
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By Heron's formulas, the area of the trapezoid is 27*sqrt(3).

Jul 29, 2020
#2
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we have (9+8+7)/2=12 and (sqrt(12(12-9)(12-8)(12-7)))/8 to find the altitude and we find that the altitude is sqrt720/8=sqrt(11.25) then we can use the pythagorean's theorem to have sqrt(49-11.25)=sqrt37.75 and (((8-2sqrt37.75)+8)*sqrt11.25)/2=8sqrt11.25-sqrt424.6875

Jul 29, 2020
#3
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What?

qwertyzz  Jul 29, 2020
#4
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Use Heron's formula to find the area of triangle ACD

12sqrt5   units squared

Use the normal area of a triangle formula to get the height

12sqrt5=1/2 * 8 *h

h= 3sqrt5

units

Let X be the point such that AX is a height

Let Y be the point such that BY is a height

(SBYX is a rectangle)

since ABCD is a isosceles trapezium, DX = YC

Find YC

YC^2 = 49-45=4

YC=DX=2

XY=AB=4

$$Area=\frac{4+8}{2}*3\sqrt5\\ area=18\sqrt5 units^2$$

You need to draw the pic and check it.

I largely did it in my head so there could easily be errors.

Jul 30, 2020