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Area of a Trapezium and a Polygon — MATHS STD 8 — Question

Gujarat BoardEnglish MediumSTD 8MATHSArea of a Trapezium and a Polygon5 Marks
Question
Find the area of pentagon $ABCDE$ in which $\text{BL}\perp\text{AC},\text{cm}\perp\text{AD}$ and $\text{EN}\perp\text{AD}$ such that $AC = 10\ cm, AD = 12\ cm, BL = 3\ cm, \ cm = 7\ cm$ and $EN = 5\ cm.$
✓

Answer

In the given pentagon $ABCDE,$
$\text{BL}\perp\text{AC},\text{CM}\perp\text{AD},\text{EN}\perp\text{AD}$
$AC = 10\ cm, D = 12\ cm, BL = 3\ cm,$
$CM = 7\ cm$ and $EN = 5\ cm,$
Area $\triangle\text{ABC}=\frac{1}{2}\text{AC}\times\text{BL}$
$=\frac{1}{2}\times10\times3=15\text{cm}^2$
Area $\triangle\text{ACD}=\frac{1}{2}\text{AD}\times\text{CM}$
$=\frac{1}{2}\times12\times7=42\text{cm}^2$
Area $\triangle\text{AED}=\frac{1}{2}\text{AD}\times\text{EN}$
$=\frac{1}{2}\times12\times5=30\text{cm}^2$
$\therefore$Area $ABCDE =$ Area $\triangle\text{ABC}\ +$ Area $\triangle\text{ACD}\ +$ Area $\triangle\text{AED}$
$=(15+42+30)\ cm ^2=87\ cm^2$.

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