Step-by-step explA triangle is a polygon which has three sides and can be categorized into the follow types:

· An equilateral triangle has equal sides and equal angles.

· An isosceles triangle has two equal sides and two equal angles.

· A scalene triangle has three unequal sides and three unequal angles.

· A right-angled triangle has one right angle (90°).

· An acute-angled triangle has all angles less than 90°.

· An obtuse-angled triangle has one angle greater than 90°.

The perimeter of a triangle = Sum of three sides

In the figure alongside of the ΔABC, the perimeter is the sum of AB + BC + AC.

Area of a triangle is given by:

A = ½ × Base × Height

Any side of the triangle may be considered as its base.

Then, the length of the perpendicular line from the opposite vertex is taken as the corresponding height or altitude.

In the figure shown above the area is thus given as: ½ × AC × BD.

Additional formulas for determining the area of a triangle:

Area of a triangle = √(s(s-a)(s-b)(s-c)) by Heron’s Formula (or Hero’s Formula), where a, b and c are the lengths of the sides of the triangle, and s = ½ (a + b + c) is the semi-perimeter of the triangle.

Area of an equilateral triangle

A= √(3) · ¼ · side, where side = a = b = c

Area of an isosceles triangle

A = ¼ ·b · √(4a2 – b2)

Area of the right angled triangle

A= ½× Product of the sides containing the right angle.

If two sides and the angle between them are given then the area of the triangle can be determined using the following formula:

Area = ½ · a · b · sinC = ½ · b · c · sinA = ½ · a · c · sin B

Example 1: Find the area of a triangle whose base is 14 cm and height is 10 cm.

## Answers ( )

Answer:Step-by-step explA triangle is a polygon which has three sides and can be categorized into the follow types:

· An equilateral triangle has equal sides and equal angles.

· An isosceles triangle has two equal sides and two equal angles.

· A scalene triangle has three unequal sides and three unequal angles.

· A right-angled triangle has one right angle (90°).

· An acute-angled triangle has all angles less than 90°.

· An obtuse-angled triangle has one angle greater than 90°.

The perimeter of a triangle = Sum of three sides

In the figure alongside of the ΔABC, the perimeter is the sum of AB + BC + AC.

Area of a triangle is given by:

A = ½ × Base × Height

Any side of the triangle may be considered as its base.

Then, the length of the perpendicular line from the opposite vertex is taken as the corresponding height or altitude.

In the figure shown above the area is thus given as: ½ × AC × BD.

Additional formulas for determining the area of a triangle:

Area of a triangle = √(s(s-a)(s-b)(s-c)) by Heron’s Formula (or Hero’s Formula), where a, b and c are the lengths of the sides of the triangle, and s = ½ (a + b + c) is the semi-perimeter of the triangle.

Area of an equilateral triangle

A= √(3) · ¼ · side, where side = a = b = c

Area of an isosceles triangle

A = ¼ ·b · √(4a2 – b2)

Area of the right angled triangle

A= ½× Product of the sides containing the right angle.

If two sides and the angle between them are given then the area of the triangle can be determined using the following formula:

Area = ½ · a · b · sinC = ½ · b · c · sinA = ½ · a · c · sin B

Example 1: Find the area of a triangle whose base is 14 cm and height is 10 cm.

Solution:

b = 14 cm

h = 10 cm

A = ½ · 14 · 10 = 70 cm2anation: