Area of Triangles: 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 Triangles 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 adds 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 Triangle = A = ½ × Base × Height(Perpendicular distance)
Area of an Equilateral Triangle
In this type of triangle all sides are equals.
Area of an Isosceles Triangle
An isosceles triangle has two sides and also two angles are equals.
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 triangles perimeter):
s = (a+b+c)/2
Process 2: Then find the Area of Triangle:
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 triangle, when we know the 2 sides and an angle of 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.
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.
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