Trapezoid

The rectangular trapezoid ABCD with a right angle at the vertex A has sides a, b, c, and d. Calculate the circumference and the area of the trapezoid if given: a = 25cm, c = 10cm, d = 8cm

Correct answer:

o =  60 cm
S =  140 cm²

Step-by-step explanation:

$$\begin{gathered} a=25\text{cm} \\ c=10\text{cm} \\ d=8\text{cm} \\ x=a-c=25-10=15\text{cm} \\ {x}^2+d^2=b^2 \\ b=\sqrt{x^2+d^2}=\sqrt{15^2+8^2}=17\text{cm} \\ o=a+b+c+d=25+17+10+8=60\text{cm} \end{gathered}$$

$S=\frac{a+c}{2}\cdot d=\frac{25+10}{2}\cdot 8=140{\text{cm}}^2$

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