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Starrysoul100

[tex]\bold{\huge{\blue{\underline{ Solution }}}}[/tex]

Given :-

  • The radius of the circle is 5 units

To Find :-

  • We have to find the area of shaded region .

Let's Begin :-

The given figure is composed of two figures triangle and circle. In which triangle is enclosed in the circle.

  • The triangle is the unshaded region of the given figure

We know that,

Area of triangle

[tex]\bold{\red{ = }}{\bold{\red{\dfrac{1}{2}}}}{\bold{\red{\times{ Base }}}}{\bold{\red{\times{ height }}}}[/tex]

Here,

  • The base of the triangle is equal to the diameter of the circle that is,
  • [tex]\sf{ Base = 5 + 5 = 10 \: units }[/tex]
  • The height of the triangle is equal to the radius of the triangle that is
  • [tex]\sf{ Height = 5 \:units }[/tex]

Subsitute the required values,

Area of the given triangle

[tex]\sf{ = }{\sf{\dfrac{1}{2}}}{\sf{\times{ 10 }}}{\sf{\times{ 5 }}}[/tex]

[tex]\sf{ = 5 }{\sf{\times{ 5}}}[/tex]

[tex]\bold{ = 25\: units }[/tex]

Thus, The area of triangle is 25 units

Now

We have to find the area of the circle

  • The radius of the circle is 5 units

We know that,

Area of circle

[tex]\bold{\pink{ = }}{\bold{\pink{\pi{r^{2}}}}}[/tex]

Subsitute the required values,

[tex]\sf{ = }{\sf{\pi{(5)^{2}}}}[/tex]

[tex]\sf{ = }{\sf{\dfrac{22}{7}}}{\sf{\times{ 25}}}[/tex]

[tex]\sf{ = }{\sf{\dfrac{550}{7}}}[/tex]

[tex]\bold{ = 78.57\: units }[/tex]

Thus, The area of circle is 78.57 units

Therefore,

Area of shaded region

= Area of circle - Area of triangle

Subsitute the required values,

[tex]\sf{ = 78.57 - 25 }[/tex]

[tex]\bold{\green { = 53.57 \: units }}[/tex]

Hence, The area of shaded region is 53.57 units.

facundo3141592

The area of the shaded figure is 13.375 square units.

What is the area of the shaded region?

The shaded region is a circle with a triangle inside of it removed.

To get the area, we need to get the area of the circle and remove the area of the triangle.

Remember that for a circle of radius R, the area:

A = 3.14*R^2

In this case, we can see that the diameter of the circle measures 5 units, then the radius (half of the diameter) measures 2.5 units.

A = 3.14*(2.5)^2 = 19.625 square units.

And a triangle of base B and height H has an area:

A' = B*H/2

In this case, the base of the triangle is equal to the diameter of the circle, and the height is equal to the radius of the circle, so we have:

B = 5 units.

H = 2.5 units.

Then:

A' =5*2.5/2 = 6.25 square units.

Then the shaded area is:

shaded area =  19.625 square units -  6.25 square units.

                     = 13.375 square units.

If you want to learn more about areas, you can read:

https://brainly.com/question/19819849

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