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