Question

Im so confused can someone help me please.

Answer 1

$\bf\huge\blue{\underline{\underline{ Question : }}}$

OAB is a sector of a circle OA = 7cm, OA = OB. Angle AOB IS 90. Calculate the shaded region.

$\bf\huge\blue{\underline{\underline{ Solution : }}}$

★ Given that,

• OAB is a sector.
• ∠O = 90°(x) .
• OA = OB = 7cm.

★ To find,

• Area of shaded region.

★ Formula used :

$\boxed{\tt{\red{ : \implies Area\:of\:shaded\:region= Area \: of \: sector - Area \: of \: triangle }}}$

$\boxed{\tt{\red{:\implies Area\:of\:Sector= \cfrac{x}{360} \times \pi r^{2} }}}$

$\boxed{\tt{\red{:\implies Area\:of\:triangle = \cfrac{1}{2} \times bh}}}$

★ Let,

➡ Find out the area of sector.

$\bf\:\implies \cfrac{90}{360} \times \cfrac{22}{7} \times 7 \times 7$

$\bf\:\implies \cfrac{ 11 \times 7}{2}$

$\bf\:\implies \cfrac{ 77}{2}$

➡ Now, find out the area of triangle.

$\bf\:\implies \cfrac{1}{2} \times 7 \times 7$

$\bf\:\implies \cfrac{49}{2}$

★ Now,

Find out the area of shaded region.

$\bf\:\implies Area\:of\:shaded\:region= \cfrac{77}{2} - \cfrac{49}{2}$

$\bf\:\implies Area\:of\:shaded\:region= \cfrac{77 - 49}{2}$

$\bf\:\implies Area\:of\:shaded\:region= \cfrac{77 - 49}{2}$

$\bf\:\implies Area\:of\:shaded\:region= \cfrac{28}{2}$

$\bf\:\implies Area\:of\:shaded\:region= 14$

$\underline{\boxed{\rm{\purple{\therefore Area\:of\:shaded\:region = 14\:cm^{2}.}}}}\:\orange{\bigstar}$

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