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Area of Triangle: Formulas & Examples


There are various ways to find the area of a triangle.

Area of a Triangle Formula

If you know the base and height of the triangle it is easy to find the area of triangle.

It is simply multiply the base by the height, and then divide by 2

And the unit of area is measured in square units in meter or cent-meter (m2, cm2).

Area of Triangle Examples

Example 1: What is the area of a triangle with base b =4  cm and height h = 5 cm?

Solution:

Using the formula of triangle,

Area of a Triangle, A = 1/2 × b × h

= 1/2 × 4 cm × 3 cm

= 2 cm × 3 cm

= 6 cm2

Example 2: Find the area of an acute triangle with a base of 10 inches and a height of 6 inches.

Solution:

Area of acute triangle (A) = (½)× b × h sq.units

⇒ A = (½) × (10 in) × (6 in)

⇒ A = (½) × (60 in2)

⇒ A = 30 in2

Example 3: Find the area of a right-angled triangle with a base of 8 cm and a height of 11 cm.

Solution:

Area = (½) × b × h sq.units

⇒ Area = (½) × (8 cm) × (11 cm)

⇒ Area = (½) × (88 cm2)

⇒ Area = 44 cm2

Area of a Right Angled Triangle

A right-angled triangle is a triangle where one angle is always 90° and left two acute angles add to 90°. Therefore, we can say the height of the right-angled triangle will be the length of the perpendicular side.

Area of a Right Angled Triangle
Area of a Right Triangle = A = ½ × Base × Height(Perpendicular distance)

Area of an Equilateral Triangle

In this type of triangle, all sides are equals.

Area of an Equilateral Triangle

Area of an Isosceles Triangle

An isosceles triangle has two sides and also two angles are equals.

Area of an Isosceles Triangle

Area of Triangle with Three Sides (Heron’s Formula)

There’s also a formula to find the area of any triangle with 3 sides of different measures. It is also called Heron’s formula.

Here are two important process:

Process 1: Find out “s” (half of the triangle’s perimeter):

s = (a+b+c)/2

Process 2: Then find the Area of Triangle:

Heron’s Formula

Example: What is the area of a triangle where every side is 6 long?

Step 1: s = (6+6+6)/2 = 9

Step 2: A = √9(9-6)(9-6)(9-6)

= √9 x 3 x 3 x 3

=√243

Triangle area for Two Sides and the Included Angle

What will be the area of a triangle, when we know the 2 sides and an angle of the triangle between two sides, then how to find its area.

For example a triangle ABC, which vertex angles are ∠A, ∠B, and ∠C, and sides are a,b and c, as given figure below.

Two Sides

For example, If, in ∆ABC,  A = 30° and b = 2, c = 4 in units. Then the area will be;

Area (∆ABC) = ½ bc sin A

= ½ (2) (4) sin 30

= 4 x ½   (since sin 30 = ½)

= 2 sq.unit.