Area of triangle
A area of triangle formula is a polygon with three sides, so here w’ll understand
Here you will learn about area of triangle (how to find area of triagle).In basic, the term “area” is defined as the region occupied inside the boundary of a flat object or figure. The measurement is done in square units with the standard unit being square meters (m2). we will learn the area of triangle formulas for different types of triangles, along with some example problems.
The area of a triangle is defined as the total region that is enclosed by the three sides of any particular triangle. Basically, it is equal to half of the base times height, i.e. AOT = 1/2 × b × h,where, b and h stands for base and hight respectively . Hence, to find the area of a tri-sided polygon, so we have to know the base (b) and height (h) of it. Then it is applicable to all types of triangles, whether it is scalene, isosceles or equilateral. To be noted, the base and height of the triangle are perpendicular to each other. The unit of area is measured in square units (m2, cm2).
Example: What is the area of a triangle with base b = 3 cm and height h = 4 cm?
Using the formula,
A = 1/2 × b × h
= 1/2 × 4 cm × 3 cm
= 2 cm × 3 cm
= 6 cm2
hence, the answer =6 cm2
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And apart from the above formula, we have Heron’s formula to calculate the triangle’s area, when we know the length of its three sides. Also, trigonometric functions are used to find the area when we know two sides and the angle formed between them in a triangle. We will calculate the area for all the conditions given here.
Area of a Triangle Formula
The area of the triangle can be easily understand by given below formula,
- Area of a Triangle = A = ½ (b × h) square units
where b and h are the base and height of the triangle, respectively.
Now, let’s see how to calculate the area of a triangle using the given formula .And The area formulas for all the different types of triangles like an area of an equilateral triangle, right-angled triangle, an isosceles triangle are given below.
Area of a Right Angled Triangle
A right-angled triangle, also called a right triangle has one angle at 90° and the other two acute angles sums to 90°. so, the height of the 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
An equilateral triangle is a triangle where all the sides are equal. The perpendicular drawn from the vertex of the triangle to the base divides the base into two equal parts. To calculate the area of the equilateral triangle, we have to know the measurement of its sides.
- Area of an Equilateral Triangle = A = (√3)/4 × side2
Area of an Isosceles Triangle
An isosceles triangle has two of its sides equal and also the angles opposite the equal sides are equal.
- Area of an Isosceles Triangle = A = ½ (base × height)
Perimeter of a Triangle
The perimeter of a triangle is the distance covered around the triangle and is calculated by adding all the three sides of a triangle.
- The perimeter of a triangle = P = (a + b + c) units
where a, b and c are the sides of the triangle.
Area of Triangle with Three Sides (Heron’s Formula)
The area of a triangle with 3 sides of different measures can be found using Heron’s formula. Heron’s formula includes two important steps. The first step is to find the semi perimeter of a triangle by adding all the three sides of a triangle and dividing it by 2. The next step is that, apply the semi-perimeter of triangle value in the main formula called “Heron’s Formula” to find the area of a triangle.
where, s is semi-perimeter of the triangle = s = (a+b+c) / 2
We have seen that the area of special triangles could be obtained using the triangle formula. However, for a triangle with the sides being given, calculation of height would not be simple. For the same reason, we rely on Heron’s Formula to calculate the area of the triangles with unequal lengths.
Triangle area for Two Sides and the Included Angle
Now, the question comes, when we know the two sides of a triangle and an angle included between them,and then how to find its area?
Let us take a triangle ABC, whose vertex angles are ∠A, ∠B, and ∠C, and sides are a,b and c, as shown in the figure below.
Now, if any two sides and the angle between them are given, then the formulas to calculate the area of a triangle is given by:
Area (∆ABC) = ½ bc sin A
Area (∆ABC) = ½ ab sin C
Area (∆ABC) = ½ ca sin B
These formulas are very easy to remember and also to calculate.
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.
Area of Triangles Examples
Find the area of an acute triangle with a base of 13 inches and a height of 5 inches.
A = (½)× b × h sq.units
⇒ A = (½) × (13 in) × (5 in)
⇒ A = (½) × (65 in2)
⇒ A = 32.5 in2
Find the area of a right-angled triangle with a base of 7 cm and a height of 8 cm.
A = (½) × b × h sq.units
⇒ A = (½) × (7 cm) × (8 cm)
⇒ A = (½) × (56 cm2)
⇒ A = 28 cm2
Find the area of an obtuse-angled triangle with a base of 4 cm and a height 7 cm.
A = (½) × b × h sq.units
⇒ A = (½) × (4 cm) × (7 cm)
⇒ A = (½) × (28 cm2)
⇒ A = 14 cm2