# 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.

A diagonal of a rectangle divides its area into two equal halves. As a result of the diagonal AC, the rectangle has been divided into two equal halves, ABC and ADC. The length DC is now considered the base of the triangle, and the breadth AD is now considered the height of the triangle in triangle ADC.

Area of a triangle ADC = (1/2) × Area of the rectangle
Area of a triangle ADC = (1/2) × DC × AB
Area of a triangle ADC = (1/2) × b × h

Know more about other concepts of Geometry on 2D Shapes, Herons Formula, Perimeter of Circle, What is Perimeter and What is Triangle.

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