Question

A circle of radius 2.1 cm is inscribed in a right-angled triangle
having sides 5 cm, 12 cm and 13 cm as shown in the figure. Find the
area of shaded region.​

Answer 1

Answer:

Area of shaded region=16.14cm^2

Step-by-step explanation:

Base=12cm

Height=5cm

Area of triangle =1/2×b×h

=1/2×12×5

=30cm^2

Area of circle =πr^2

=22/7×(2.1)^2

=22/7×2.1×2.1

=22×0.3×2.1

=13.86 cm^2

Area of shaded region =Area of triangle-Area of circle

=30cm^2-13.86cm^2

=16.14cm^2

Hope it's help u!!

Answer 2

${\underline{\underline{\sf{Given:}}}}$

• A right-angled triangle whose measures are 13 cm, 5 cm and 12 cm.
• A circle of radius 2.1 cm is inscribed inside the right-angled triangle.

${\underline{\underline{\sf{Need\:to\:find:}}}}$

• The area of shaded region (attachment).

${\underline{\underline{\sf{Formulae\:to\:be\:used:}}}}$

$\underline{\boxed{\sf{{Area}_{(Right-angled\: triangle)}=\frac{1}{2}\times (Base\times Leg)\:sq.units}}}$

$\underline{\boxed{\sf{{Area}_{(Circle)}=\pi {r}^{2}\:sq.units}}}$

$\underline{\boxed{\sf{{Area}_{(Shaded\:region)}={Area}_{(Right-angled\: triangle)}-{Area}_{(Circle)}\:sq.units}}}$

${\underline{\underline{\sf{Solution:}}}}$

First, let's find the area of right-angled triangle by substituting the given measures in the formula.

$\:\:\:\:\:\implies{\sf{\frac{1}{2}\times (Base\times Leg)\:sq.units}}$

$\:\:\:\:\:\implies{\sf{\frac{1}{2}\times (12\times 5)\:{cm}^{2}}}$

$\:\:\:\:\:\implies{\sf{\frac{1}{\cancel{2}}\times \cancel{60}\:{cm^{2}}}}$

$\:\:\:\:\:\implies{\sf{\underline{30\:{cm}^{2}}}}$

Next, let's find the area of circle by substituting the measures in the formula.

$\:\:\:\:\:\implies{\sf{\pi{r}^{2}\:sq.units\:\:\:(\pi=\frac{22}{7})}}$

$\:\:\:\:\:\implies{\sf{\frac{22}{7}\times{(2.1)}^{2}\:{cm}^{2}}}$

$\:\:\:\:\:\implies{\sf{\frac{22}{7}\times4.41\:{cm}^{2}}}$

$\:\:\:\:\:\implies{\sf{\underline{13.86\:{cm}^{2}}}}$

Finally, the area of shaded region:

$\:\:\:\:\:\implies{\sf{Area\:of\: right\:angled\: triangle-Area\:of\:circle\:sq.units}}$

$\:\:\:\:\:\implies{\sf{30-13.86\:{cm}^{2}}}$

$\:\:\:\:\:\implies{\sf{\red{\underline{\underline{16.14\:{cm}^{2}}}}}}$

${\underline{\underline{\sf{Final\:answer:}}}}$

• The area of the shaded region is $\bf{16.14\:{cm}^{2}}$.

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