**Introduction :-**

In this article we are going to see about learning combining shapes topics and problems involving it. The majority of the shapes of buildings lakes and the commonplace things around us are always in a learning combining shapes. Near locate the perimeter area and volume of these learning combining shapes, we usually use geometry. Geometry has formulas that rally round us to find the perimeter, area and volume of anything that we see.

**Learning combining shapes perimeter:-**

Consent us have a building in the shape of a rectangle and semi-circle attached to one width.

Get the perimeter of the building.

Because one width is attached to the diameter of semi-circle, we cannot get that width into account

So the perimeter would be 2 lengths + 1 width + circumference of half the circle

Formula for circumference of semi-circle is πr where r is radius of the semi-circle.

During this case radius is half the width

So the perimeter of the rectangle-semicircle building is 2 length+1 width+ π times half the width.

Let the length of the rectangle be 8 inches and width 6 inches.

Then Perimeter of the combined shape is

2(8) + 6 inches for rectangle plus π times 2 inches (half the width)

=16+6+3.14 x 2

=22 +6.28

= 28.28 inch.

**Learning combining shapes perimeter:-**

Here these building two sides of the square cannot be taken into account.

So the perimeter would the length of the remaining two sides + the circumference of two semi-circles.

We have to remember that two semi-circle equal’s one full circle and the side of the square becomes diameter.

So the perimeter of this building would be length of two sides + circumference of the circle

That would amount to length of two sides + πd where d is diameter and here d is the surface of square

So the perimeter is length of two sides of the square + π times’ one side of the square.

Allow the side of the square be 6 inches.

Then 6 + 6 + π times 6

= 12 + 3.14 x 6

= 12 + 18.84

=30.84 inch.

**Learning combining shapes of area:-**

Suppose we are asked to find the area of a park, which is a combination of a rectangle and semi-circle,

We have to find the area of the rectangle and the area of the semicircle and add them both

Area of the rectangle is length times width and area of the semi-circle is half the value of πr^{2} where r is half the width.

So combination of 2 areas would be length x width + π times (width)^{2}/ 2

Area of rectangle is 6 times 4 = 24 square inch.

Area of semicircle with radius 3 inch is π times 2^{2} = 3.14 x 4=12.56 sq inches.

Adding both 24 + 12.56 we get 36.56 sq inches as area of the park.

**Learning combining shapes volume:-**

This is the majority attractive aspect in combined form.

Volume of the cylinder is πr^{2}h where r is the radius of the cylinder and h is height of the cylinder.

Volume of sphere is (4πr^{3})/3 where r is radius of sphere.

So volume of the doll would be πr^{2}h + (4πr^{3})/3

Let the radius of the cylinder be 3 inches and height be 12 inches.

Then volume of the cylinder is π times 2^{2} x 12

= 48 x 3.14

= 150.70 cu inch.

The volume of the sphere is (3 times π x 2^{3})/ 3

= (3x3.14 x 8)/3

=25.12 cu inch.

Adding both we get 150.70 + 25.12 =175.82 cu inch.

**Learning combining shapes problem:-**

Let us notice the above picture.

That of a model with half sphere as base and reversed cone as a body.

Here the volume of half sphere is (2πr^{3})/3 and the volume of the cone is (πr^{2}h)/3

Let the radius of the cone be 6 inches and height 12 inches

Since the volume of the cone is one-third of the volume of cylinder

=226.60/3

=75.36 cu inch.

The volume of semi-sphere is = 38.62/2 = 19.31 cu inches.

Add both 75.87 + 19.31 = 95.18 cu. Inch.