Area and Perimeter: Overview, Questions, Preparation

Area and perimeter is an important concept for any geometrical shape and figure. We can calculate the space occupied by that shape and the boundaries. In real life, these concepts are used widely in terms of construction or measuring the fence boundary. Different geometrical shapes have different formulas to calculate the area and perimeter. In the below figure, you can see the area of different shapes.

 Source: NCERT

What is the Topic all About?

The topic speaks about the basic characteristics of any geometrical shape and their uses in our day-to-day life. For example, before constructing any building, the architect needs to figure out the building's area and perimeter to build walls and flooring purposes.

What are the Various Aspects that Form Part of the Topic?

Area and perimeter calculation need the fundamental knowledge of the geometric shapes that are being used. The different concepts required to calculate the area and perimeter of any given shape are faces, angles, side length, number of sides and more.

What are Some Different Types of Area and Perimeters?

Areas and perimeters are mensuration concepts that occupy the centre stage in any construction works. The area is the total space covered inside the boundary of the shape. Perimeter is the total length of the exterior boundaries of the given shape. Hence, we can have circles, triangles, rhombus, trapezium, parallelogram, square, rectangle, decagon and more.

Area and Perimeter topics are introduced in the 8t^h NCERT maths book in the chapter' 'Mensuration'. The idea of areas is introduced with many examples, such as the walls and brick example to quantify the meaning of space covered by boundaries. Perimeter is also important as it measures the total length of the shape boundary. The exam questions revolve around this topic and have a weightage of around 5% to 15%. The topic has a weightage of around 5% to 15%.

1. Find the area of the given quadrilateral PQRS.

(Source: NCERT)

Solution. 

In the given case, d = 5.5 cm,
h1 = 2.5cm, h2 = 1.5 cm,
Area = 1/2 * d ( h1 + h2 )
= 1 2 × 5.5 × (2.5 + 1.5) cm^2
= 1 2 × 5.5 × 4 cm^2 = 11 cm^2

2. Find the rhombus area whose diagonals are of lengths 10 cm and 8.2 cm.
Solution.

Area of the rhombus = 1/2/* d1* d2
Where d1 and d2 are lengths of diagonals of the rhombus.
= 1/2 × 10 × 8.2 cm^2 = 41 cm^2

3. The rhombus area is 240 cm^2, and one of the diagonals is 16 cm. Find the other diagonal.
Solution. 

One diagonal length (d1) = 16 cm & other diagonal length = (d2)
Hence, rhombus area = 1/2 *d1* d2 = 240
So, 1/2 *16* d = 240 Therefore, d2 = 30 cm

Q: How many sides are needed to calculate the area of regular heptagon?

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Q: Can the diagonals be used to calculate the area?