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

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

x=17

step-by-step explanation:

solve 3x-24=x+10

then that makes it 2x=34 because you subtract an x from both sides to get rid of the one on the right, and then you add 24 to both sides to get rid of the 24 on the left

divide by both sides by 2 to get your answer so that you can get your answer

not me

step-by-step explanation:

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