The trapezium

The trapezium is formed by cutting the top of the right-angled isosceles triangle. The trapezium base is 10 cm, and the top is 5 cm. Find the area of the trapezium.

Final Answer:

A =  18.75 cm²

Step-by-step explanation:

$$\begin{gathered} b_1=10\text{cm} \\ {b}_2=5\text{cm} \\ {a}_1^2+a_1^2=b_1^2 \\ {a}_2^2+a_2^2=b_2^2 \\ {a}_1=b_1/\sqrt{2}=10/\sqrt{2}=5\sqrt{2}\text{cm}\doteq 7.0711\text{cm} \\ {a}_2=b_2/\sqrt{2}=5/\sqrt{2}\doteq 3.5355\text{cm} \\ {A}_1=\frac{a_1^2}{2}=\frac{7.0711^2}{2}=25{\text{cm}}^2 \\ {A}_2=\frac{a_2^2}{2}=\frac{3.5355^2}{2}=\frac{25}{4}=6.25{\text{cm}}^2 \\ A=A_1-A_2=25-\frac{25}{4}=\frac{25\cdot 4}{4}-\frac{25}{4}=\frac{100}{4}-\frac{25}{4}=\frac{100-25}{4}=\frac{75}{4}=\frac{75}{4}{\text{cm}}^2=18.75{\text{cm}}^2 \end{gathered}$$

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