What is the area of a trapezoid which its inferior base is 10",the superior base is 4",and each of the sides has 5",have the same interior opposite angles?

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Answer 1 · 2018-04-29T03:35:04

#color(blue)("Area of Trapezoid " = (1/2) * (10 + 4) * 4 = 28 " sq inch"#

#bar (AB) = 4 "inch", bar(CD) = 10"inch", bar (BC) = bar(AD) = 5"inch"#

To find area of the trapezoid.

Let AE = BF be the height of the trapezoid.

#DE = CF = (CD - AB ) / 2 = (10 - 4) / 2 = 3 "inch"#

#bar (AE) = bar (BF) = sqrt((AD)^2 - (DE)^2) = sqr(5^2 - 3^2) = 4 "inch"#

#"Area of Trapezoid " = (1/2) * (AB + CD) * (AE)#

#color(blue)("Area of Trapezoid " = (1/2) * (10 + 4) * 4 = 28 " sq inch"#