Area of Rectangle, Square and Triangle

Area of a closed plane figure is the amount of surface enclosed within its boundary.

Look at the given figures. 

The shaded region of each figure denotes its area. The standard unit, generally used for measuring the area, is square centimetre or square metre.

Area of a Square of Side 1 cm

The area of a square of side 1 cm is 1 square centimetre. We write it as 1 sq. cm or 1 cm²

Similarly, the area of a square of side 1 metre is 1 square metre. We write it as 1 sq. m or 1 m².

Area of a Rectangle:

Let us consider a rectangle ABCD whose length and breadth are 4 cm and 2 cm respectively.

To find the area of the rectangle, we divide it into squares of 1 cm² area i.e., squares of 1 cm × 1 cm . We can divide it in 8 such squares.

So, the area of the rectangle ABCD = 8 cm², which is the product of the length and breadth of the given rectangle.

Area of the given rectangle = 4 cm × 2 cm = 8 cm²

Area of a rectangle = length × breadth

Area of a Square:

Let us consider a square of 3 cm side.

If we divide it into square of 1 cm² we get 9 such squares. So, the area of the given square is 9 cm² which is the product of the two sides of the given square.

Area of the given square = 3 cm × 3 cm = 9 cm²

Remember: The product of two equal number is also called (number)². (3 × 3 = 3² = 9)

Area of a square = side × side = (side)²

Area of a Triangle:

If the base of a triangle ABC is 4 cm and its height is 3 cm, the area will be

$\frac{\textrm{base × height}}{2}$

= $\frac{4 × 3}{2}$

= 6 cm²

Area of a triangle = $\frac{\textrm{base × height}}{2}$

Let us Consider Some Examples on Area of Rectangle Square and Triangle:

1. Find the area of a rectangle having length 12 cm and breadth 8 cm.

Solution:

Area of a rectangle = length × breadth  

                            = 12 cm × 8 cm

                            = 96 cm²

2. Find the area of a square board having sides 8 cm each.

Solution:

Side of square = 8 cm

Area of square = side × side

                      = 8 cm × 8 cm

                      = 64 cm²

3. Area of a rectangular field is 108 cm². Its length is 12 cm. Find its breadth.

Solution:

Area of the rectangular field = 108 cm²

Length of the rectangular field = 12 cm

Area of th e rectangular field = length × breadth

                              Breadth = $\frac{\textrm{Area}}{\textrm{Length}}$

                                          = $\frac{108}{12}$ cm

                                          = 9 cm

4. Find the area of a triangle having base 7 cm and height 4 cm

Solution:

Area of a triangle = $\frac{\textrm{base × height}}{2}$

                          = $\frac{7 × 4}{12}$ cm²

                          = 14 cm²

5. Area of a triangle is 48 cm². If its base is 16 cm, find its height.

Solution:

Area of triangle = $\frac{\textrm{base × height}}{2}$

             Height = $\frac{\textrm{2 × Area}}{Base}$

                       = $\frac{\textrm{2 × 48}}{16}$ cm

                       = $\frac{96}{16}$ cm

                       = 6 cm

Area of Four Walls of a Room:

A room has length, breadth and height. It has four walls a pair of lengthwise walls and a pair of breadthwise walls.

Suppose, ℓ, b and h be the length, breadth and height of the walls.

Area of four walls of a room can be found as follows.

Total area = Area of 2 lengthwise walls + area of 2 breadthwise walls

               = ℓ × h + ℓ × h + b × h + b × h + b × h

               = 2ℓh + 2bh

               = 2h(ℓ + b)

So, the area of four walls of a room = 2h(ℓ + b) sq. units.

Example on Area of Four Walls of a Room:

1. The length, breadth and height of a room is 8 m, 9 m and 14 m respectively. Find the area of the room.

Solution:

Area of the room = 2h(ℓ + b)

Here, ℓ = 8 m, b = 9 m and h = 14 m

So, area of the room = 2h(ℓ + b)

                               = 2 × 14 m (8 m + 9 m)

                               = 28 m × 17 m

                               = 476 m²

5th Grade Geometry

5th Grade Math Problems

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