In the given figure, the grid consists of unit squares. What is the area of the polygon?

7

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9

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12

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15

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Solution

The correct option is D $15$
$∵ T h e s q u a r e s a r e u n i t o n e s ⟹ o n e s i d e = 1 u n i t . N o w t h e 4 s i d e d p o l y g o n h a s t w o o p p o s i t e s i d e s ∥ e a c h o t h e r . ∴ I t i s a t r a p e z i u m . W e s h a l l f i n d o u t t h e d i f f e r e n t l e n g t h s b y c o u n t i n g t h e s i d e s o f t h e g r i d . I t s t w o p a r a l l e l s i d e s a r e o f 3 u n i t s & 7 u n i t s ∴ s u m o f t h e p a r a l l e l s i d e s = (3 + 7) u n i t s = 10 u n i t s . A l s o t h e h e i g h t = 3 u n i t s ∴ a r (t r a p e z i u m) = \frac{1}{2} (s u m o f t h e p a r a l l e l s i d e s) (h e i g h t) = \frac{1}{2} \times 10 \times 3 s q u n i t s = 15 s q u n i t s . A n s - O p t i o n D .$

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