Mensuration

Perimeter is an important property of a closed figure as it gives an idea about the size of the figure. The given video explains the basic concept involved in calculating the perimeter of any closed figure.

Let us now discuss some more examples based on the perimeter of closed figures.

**Example 1:**

**Find the perimeter of the following figures.**

**(a)**

**(b)**

**Solution:**

**(a)** Perimeter of the given figure = PQ + QR + RS + ST + TP

= 20 cm + 15 cm + 18 cm + 26 cm + 21 cm

= 100 cm

**(b)** Perimeter of the given figure = LM + MN + NO + OP + PQ + QL

= 3.5 cm + 2.75 cm + 6.25 cm + 6.0 cm

+ 2.25 cm + 4.0 cm

= 24.75 cm

**Example 2:**

**The lengths of three sides of a quadrilateral are 10.6 cm, 12.7 cm, and 9.2 cm. If the perimeter of the quadrilateral is 46.9 cm, then what is the length of the fourth side?**

**Solution:**

We know that,

Perimeter of the quadrilateral = Sum of four sides of quadrilateral

⇒ Perimeter of the quadrilateral = Sum of three sides of quadrilateral + Fourth side

⇒ 46.9 cm = (10.6 cm + 12.7 cm + 9.2 cm) + Fourth side

⇒ 46.9 cm = 32.5 cm + Fourth side

Thus, fourth side = 46.9 cm – 32.5 cm

= 14.4 cm

**Example 3:**

**What is the cost of fencing a pentagon-shaped land of sides 75 m, 47 m, 18 m, 39 m, and 31 m at the rate of Rs 8 per metre?**

**Solution:**

To find the cost of fencing the land, we have to find out the perimeter of the pentagon-shaped land.

Perimeter of the pentagon-shaped land = Sum of five sides of the pentagon

= 75 m + 47 m + 18 m + 39 m + 31 m

= 210 m

Cost of fencing = Rs 8 per metre

∴Cost of fencing 210 m of the boundary = Rs (8 × 210) = Rs 1680

Thus, the cost of fencing the pentagon-shaped land is Rs 1680.

Look at the following figures.

**What do we observe in these figures?**

It can be observed that all the sides of the given figures are equal. These types of figures are known as **regular polygons.**

The first, second, and third figures are the figures of an equilateral triangle,...

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