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3 years ago

Given: ABCD is a trapezoid, AB = 13,CD = 14, BC = 5, and AD = 20. Find: A of ABCD

Mathematics

1 answer:

Nostrana [21]3 years ago

4 0

Answer:

140 cm²

Step-by-step explanation:

A trapezoid consists of one rectangle and two triangles.

Now ABCD is a trapezoid. Consider two heights BE and CF.

Therefore,l BEFC will be a rectangle,

then, EF and BC would be equal and BE and CF will be equal.

EF = BC = 5 and BE = CF = y.

Considering AE as 'x', then

FD = AD - AE - EF

FD= 20 - x - 5 => 15 - x.

Below the attactment you can see, Triangles ABE and CDF are two right triangles. Applying the Pythagorean theorem,

AB² = BE² + AE² => 13² = y² +x² ---> eq(1)

CD² = CF² + DF² => 14²= (15-x)²+ y²--->eq(2)

subtract eq (1) from eq (2)

14²-13² =(15-x)²-x²----> (term y² cancelled)

196 - 169 = 225 - 30x + x²- x² ----> (term x² cancelled)

30x= 225 - 196 + 169

30x = 198

x= 198/30 => 6.6

putting the above value in eq(1)

169= 6.6² + y²

y² = 169 - 43.56

y²= 125.44 ---> taking sqare root on both sides

y= 11.2

Area of trapezoid can be determined by

A= (5+20)/2 . 11.2 = 140

Therefore Area of trapezoid is 140 cm²

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