Rectangular trapezoid

Calculate the content of a rectangular trapezoid with a right angle at the point A and if |AC| = 4 cm, |BC| = 3 cm and the diagonal AC is perpendicular to the side BC.

Result

S =  9.84 cm2

Solution:

∣AB∣=32+42=5 S1=S2 3⋅4/2=5h/2 h=3⋅4/5=2.4 cm=∣AD∣=∣CX∣ ∣BX∣2=32−h2 ∣BX∣=9−2.42=1.8 cm ∣CD∣=∣AB∣−∣BX∣=5−1.8=3.2 cm  S=∣CD∣⋅h+h⋅∣BX∣/2=9.84 cm2|AB| = \sqrt{ 3^2 + 4^2 } = 5 \ \\ S_1 = S_2 \ \\ 3\cdot 4/2 = 5 h /2 \ \\ h = 3\cdot 4/5 = 2.4 \ cm = |AD| = |CX| \ \\ |BX|^2 = 3^2 - h^2 \ \\ |BX|= \sqrt{ 9 - 2.4^2 } = 1.8 \ cm \ \\ |CD| = |AB| - |BX| = 5 - 1.8 = 3.2 \ cm \ \\ \ \\ S = |CD|\cdot h + h \cdot |BX|/2 = 9.84 \ cm^2

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