Practice Questions on Area of Triangle

Area of a triangle is given by Heron’s formula. Let ABC be a triangle such that the length of 3 sides of the triangle is AB = c, BC = a and AC = b. Then, the area of triangle ABC(△),

△ = √[s (s – a)(s – b)(s – c) where s is semi-perimeter calculated by (a + b + c) / 2.

In this article, we will explore the area of a triangle and practice Questions on the Area of the triangle and others in detail.

What is a Triangle?

Polygon with three sides is called a triangle. The different types of triangles include:

Formula Used

Various formulas used for calculating areas of the triangle are added in the table below:

Types of Triangles	Formulas
Area of Equilateral Triangle	(√3 / 4) a²
Area of Isosceles Triangle	(b / 2) √[a² – (b²/4)]
Area of Scalene Triangle	√[s (s – a) (s – b) (s – c)
Area of Right-Angled Triangle	(1/2) × b × h

where,

a is side of Equilateral Triangle
a is equal side and b is base of isosceles Triangle
s is Semi-perimeter of Triangle and is equal to (a + b + c)/2
b is base and h is Height of Right Triangle

Practice Questions on Area of Triangle

Question 1: Find the area of the equilateral triangle with side length 11 units.

Solution:

Area of the equilateral triangle with side a is given by:

Area of Equilateral Triangle = (√3/4)a²

= (√3/4) 11²

= (√3 / 4)(121)

= 52.4 square units

Question 2: Find the area of isosceles triangle with two sides of length 7 units and base of length 12 units.

Solution:

Area of the isosceles triangle with equal side a and base b is given by:

Area of Isosceles Triangle = (b / 2) √[a² – (b²/4)]

= (12 / 2) √[7² – (12²/4)]

= 6 √[49 – 36]

= 6√13 square units

Question 3: Find the area of the scalene triangle with sides 4, 7, 5 units.

Solution:

Area of the scalene triangle is given by:

Area of Scalene triangle = √[s (s – a) (s – b) (s – c) where, s = (a + b + c) / 2

s = (4 + 7 + 5) / 2 = 16 /2 = 8 units

= √[8 (8 – 4) (8 – 7) (8 – 5)

= √[8 × 4 × 1 × 3]

= √96 square units

Question 4: Find the area of the right-angled triangle with base and height 10 units and 5 units respectively.

Solution:

Area of the right-angled triangle is given by:

Area of Right-Angled Triangle = (1/2) × b × h

= (1/2) × 10 × 5

= 25 square units

Question 5: Calculate the area of a triangle with base 6 cm and height 8 cm.

Solution:

Area = (1/2) × base × height

= (1/2) × 6 cm × 8 cm

= 24 square cm

Question 6: The base of a triangle is 10 meters and its height is 15 meters. What is the area of the triangle?

Solution:

Area = (1/2) × base × height

= (1/2) × 10 meters × 15 meters

= 75 square meters

Question 7: Given the vertices of a triangle as (-3, 4), (1, -2), and (5, 6), determine its area.

Solution:

Use the formula for the area of a triangle given its vertices.

Area = (1/2) × |x₁(y₂ – y₃) + x₂(y₃ – y₁) + x₃(y₁ – y₂)|

= (1/2) × |(-3)(-2-6) + 1(6-4) + 5(4-(-2))|

= (1/2) × |(-3)(-8) + 1(2) + 5(6)|

= (1/2) × (24 + 2 + 30)

= (1/2) × 56 = 28 square units

Question 8: Find the area of an equilateral triangle with side length 9 cm.

Solution:

Area = (√(3)/4) × side²

Area = (√(3)/4) × (9)

= (√(3)/4) × 81

= (81sqrt(3))/4

≈ 39.59 square cm

Worksheeet on Area of Triangle

Q1: Find the area of the equilateral triangle with side length 24 units.

Q2: Find the area of isosceles triangle with two sides of length 13 units and one side of length 20 units.

Q3: Find the area of the scalene triangle with sides 12, 13, 21 units.

Q4: Find the area of the right-angled triangle with base and height 11 units and 17 units respectively.

Q5: A triangle has sides of length 7 cm, 10 cm, and 14 cm. What is its area?

Q6: If the area of a triangle is 36 square inches and its base is 12 inches, what is its height?

Q7: Calculate the area of a right-angled triangle with legs measuring 3 meters and 4 meters.

Q8: Find the area of a triangle with vertices at (0, 0), (4, 0), and (0, 6).

Frequently Asked Questions

What is Area of Triangle with 3 Sides Definition?

Area of triangle with 3 sides can be defined as the area of triangle with all 3 different sides i.e., scalene triangle.

What is Formula Used to Calculate Area of Triangle with 3 Sides?

Formula used to calculate area of triangle with 3 sides is given by Heron’s formula.

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