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Areas Related to Circles — Maths STD 10 — Question

Maharashtra BoardEnglish MediumSTD 10MathsAreas Related to Circles3 Marks
Question
In the given figure, ABCD is a trapezium with $\text{AB}||\text{DC},\text{AB}=18\text{cm}$ DC = 32cm and the distance between AB and DC is 14cm. Circles of equal radii 7cm with centres A, B, C and D have been drawn. Then find the area of the shaded region.$\Big(\text{Use }\pi=\frac{22}{7}\Big)$
✓

Answer

In trapezium ABCD
$\text{AB } || \text{ DC}$
AB = 18cm, DC = 32cm Height = 14cm
Radius of each at the corner of trapezium = 7cm

$\therefore$ Angle of a quadrilateral $=360^\circ$
$\therefore$ 4 sectrors compete a circle
$\therefore$ Angle of a circle $=\pi \text{r}^2=\pi\cdot(7)^2=\frac{22}{7}\times49\text{cm}^2$
$=154\text{cm}^2$
and area of trapezium
$=\frac{1}{2}(\text{AB}+\text{DC)}\times\text{h}$
$=\frac{1}{2}(18+32)\times14\text{cm}^2$
$=\frac{1}{2}\times50\times14=350\text{cm}^2$
$\therefore$ Area of shaded portion
$= 350 - 154 = 196\text{cm}^2$

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