Question

Find the perimeter and area of the shaded region in the following figures. All measurements all in centimeters.
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Answer 1

Answer:

hello,

I will try my best to answer you in such a manner that u can understand the solution easily.

Answer to the 1st part:

If you observe the diagram,

You can see that the diagram of the 1st part is made up of two shapes

one is semi-circle and the other is rectangle.

Now in the diagram the measurement of the rectangle is given, Right!

the length is given as 10.5cm and the breath is given as 4cm.

So you firstly calculate the area and perimeter of the rectangle.

calculation of the rectangle:

AREA: l * b

         = 10.5 * 4 = 42cm^2

PERIMETER: 2(l + b)

                   = 2(4+10.5) =29 cm

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So now half the question is completed,Correct!

so lets complete the question,

Now we have to find the perimeter and area of semi-circle to find the complete diagram's perimeter and area.

so if you observe carefully,

the part of the rectangle on which the diameter of semi circle is overlying is the length of the rectangle of total lenght 10.5 cm...okkay

so from this u can find the diameter of the semi-circle.

Diameter:

=(10.5 - 3.5)cm = 7cm

hence, the radius = diameter\2 = 7\2 = 3.5cm.

Now find the area and perimeter of the semi circle:

Area: Pie * Radius* Radius

        = 22\7 * 3.5* 3.5 = 38.5cm^2

Perimeter: 2* Pie* Radius

            = 2* 22/7 * 3.5 = 22cm

Now , add the perimeter of the rectangle to the perimeter of the semi-circle to find the perimeter of the complete diagram.

Total Perimeter= Perimeter of the rectangle + Perimeter of the semicircle

                          = 29 cm + 22cm = 51cm

Now find the area of whole diagram using the same process, i.e , add the area of rectangle to area of semi circle.

 Total Area= Area of the rectangle + Area of the semicircle

                    = 42cm^2 + 38.5cm^2 =  80.5 cm^2

This how we will solve this question,

I hope I am successful at understanding u how to solve this question.

Now, I leave the second part for u solve:)

Good Luck *-*