What is Area of triangle
Answers
Answer:
The area of a triangle is defined as the total space that is enclosed by any particular triangle. The basic formula to find the area of a given triangle is A = 1/2 × b × h, where b is the base and h is the height of the given triangle, whether it is scalene, isosceles or equilateral.
Example: To find the area of the triangle with base b as 3 cm and height h as 4 cm, we will use the formula for:
Area of a Triangle, A = 1/2 × b × h = 1/2 × 4 cm × 3 cm = 2 cm × 3 cm = 6 cm2
Table of Content
Formulas
Right Angled Triangle
Equilateral Triangle
Isosceles Triangle
Perimeter
Heron’s Formula
Examples
FAQ’s
In general, 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). For the computation of area, there are pre-defined formulas for squares, rectangles, circle, triangles, etc.
Area Of Isosceles Triangle
Area Of Scalene Triangle
Area Of Similar Triangles
Properties Of Triangle
In this article, we will learn the area of triangle formulas for different types of triangles, along with some example problems.
Area of Triangle
Area of a Triangle Formula
The area of the triangle is given by the formula mentioned below:
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 formulas. 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. Also, how to find the area of triangle with 3 sides using Heron’s formula with examples.
Area of a Right Angled Triangle
A right-angled triangle or also called a right triangle have one angle at 90° and the other two acute angles sums to 90°. Therefore, the height of the triangles 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
An equilateral triangle has all its sides as 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 a equilateral triangle
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 angle opposite the equal sides are equal.
area of an isosceles triangle
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 as the sum of all the three sides of it.
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 3 Sides using Heron’s Formula
The area of a triangle with 3 sides 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 when all the measurement of three sides of a triangle are given. The next step is that, apply the sides measures of a triangle, such as a, b, and c and the semi-perimeter of triangle value in the main formula called “Heron’s Formula” to find the area of a triangle.
Area of triangles for three sides-Heron's formulawhere, s is semi-perimeter of the triangle = (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 usually, calculation of height would not be simple. For the same reason, we rely on Hero’s Formula to calculate the area of the triangles with unequal lengths.
Area of Triangles Examples
Example 1:
Find the area of an acute triangle with a base of 13 inches and a height of 5 inches.
Solution:
A = (½)× b × h sq.units
⇒ A = (½) × (13 in) × (5 in)
⇒ A = (½) × (65 in2)
⇒ A = 32.5 in2
Example 2:
Find the area of a right-angled triangle with a base of 7cm and a height of 8cm.
Solution:
A = (½) × b × h sq.units
⇒ A = (½) × (7 cm) × (8 cm)
⇒ A = (½) × (56 cm2)
⇒ A = 28 cm2
Example 3:
Find the area of an obtuse-angled triangle with a base of 4cm and a height 7cm.
Solution:
A = (½) × b × h sq.units
⇒ A = (½) × (4 cm) × (7 cm)
⇒ A = (½) × (28 cm2)
⇒ A = 14 cm2
Answer:
1/2×base×height
Step-by-step explanation:
I hope it helps you