# Perimeter and Area of Triangle

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The perimeter of any polygon is equal to the sum of the lengths of all of its sides or edges. Hence the perimeter of a triangle is equal to the sum of the lengths of its three sides.

If a triangle has sides of lengths a, b, and c units, then the perimeter of the triangle

P = (a + b + c) units.

Example 1: Find the perimeter of a triangle whose sides are of lengths 5 cm, 7 cm, and 9 cm.

Solution: Perimeter of the triangle = 5 cm + 7 cm + 9 cm = 21 cm

Example 2: Find the length of the base of the triangle whose perimeter is 36 in and the lengths of the other two sides are given in the figure below.

Solution:
Perimeter of triangle = length (XY) + length (YZ) + length (XZ)
⇒ 36 in = 8 in + 12 in + length (XZ)
⇒ length (XZ) = 36 – (8 + 12) = 16 in
⇒ length (XZ) = 16 in

Example 3: Find the perimeter of an equilateral triangle whose side is of length 5 ft.

Solution: Perimeter, P = 3a = 3 × 5 = 15 ft.

Example 4: A triangular park has dimensions of 20 m, 56 m, and 75 m. Jacob decides to cover the park with a fence. What is the length of the fence needed to completely cover the park?

Solution: The perimeter of the triangular park is 20 m + 56 m + 75 m = 151 m.
Jacob needs 151 m of fence to cover the triangular park.

## Area of a Triangle

The area of a triangle is the area bounded by its three sides. Let us consider the length of the base of a triangle to be ‘b’ and the height of a triangle to be ‘h’.

Area of a triangle = 1/2×b×h sq. units

How do you prove that the area of a triangle is equal to 1/2×b×h sq.units?

Consider a rectangle which is cut across its diagonal; it forms two right angled triangles. Refer to the image given below.