Area

Area

  • Area is the total amount of surface enclosed by a closed figure.

Area of Square

  • Area of a square = Side × Side = Side2 = {{\rm{a}}^2}, where a is the length of each side.  

Example

Calculate the area of a square of side 13 cm.

Solution

Area of a square = side × side

= 13 × 13

= 169 {\rm{c}}{{\rm{m}}^2}.

Area of Rectangle

  •  Area = length (l) × breadth (b)

Example

Find the area of a rectangle whose length and breadth are 20 cm and 12 cm respectively.

Solution

Length of the rectangle = 20 cm

Breadth of the rectangle = 12 cm

Area of the rectangle = length × breadth

= 20 cm × 12 cm

= 240 sq. cm.

Area of a triangle

Area of triangle = \left( {\dfrac{1}{2}} \right) × base × height = \left( {\dfrac{1}{2}} \right)× b × h

Areas of different types of triangles

Consider an acute and an obtuse triangle.
Area of each triangle = \left( {\dfrac{1}{2}} \right) × base × height = \left( {\dfrac{1}{2}} \right) × b × h

Visualization of Area

  • In the given graph, if the area of each small square is 1 cm2, then
    Area of rectangle  = {\rm{ l}} \times {\rm{b }} = {\rm{ }}5 \times 2{\rm{ }} = {\rm{ }}10{\rm{c}}{{\rm{m}}^2}
    Area of square  = {\rm{ a}} \times {\rm{a }} = {\rm{ }}2 \times 2{\rm{ }} = 4{\rm{c}}{{\rm{m}}^2}

Area of irregular shapes

The area of an irregular figure can be calculated by:

Step 1: Divide the irregular shape into regular shapes that you can recognize (eg. triangles, rectangles, circles, and squares)
Step 2: Find the area of these individual shapes and add them. The sum will be the area of the irregular figure.

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