Calculate the area of this figure by forming triangles.
Ans:78.5m^2
Answers
Answer:
Step-by-step explanation:
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 formula. 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 a triangle with 3 sides using Heron’s formula with examples.
Also, read:
Area Of Isosceles Triangle
Area Of Scalene Triangle
Area Of Similar Triangles
Properties Of Triangle
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°. Therefore, the height of the 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
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 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 angles 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 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.
Area of triangles for three sides-Heron's formulawhere, 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, 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.
triangle ABC vertices and sides
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
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 7 cm and a height of 8 cm.
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 4 cm and a height 7 cm.
Solution:
A = (½) × b × h sq.units
⇒ A = (½) × (4 cm) × (7 cm)
⇒ A = (½) × (28 cm2)
⇒ A = 14 cm2