In this article, we will learn the area of triangle formulas for different types of triangles, along with some examples.
The “Area of Triangle” is the measure of the region enclosed by the three sides of the triangle. As we know, a triangle is a closed shape that has three sides, three vertices and three angles. Thus, the area of triangle is the total space occupied within the three sides of a triangle.
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What is Area of Triangle?
The area of triangle is the region enclosed by it, in a two-dimensional plane. The basic formula for the area of triangle is equal to half the product of its base and height, i.e., Area= ½×B×H, where B means base and H means height.
Area of Triangle Formulas-
Here are some common formulas for finding the area of a triangle, along with example:
1.Using base and height:
Area=½×Base ×Height
Example: If the base of a triangle is 6 units and the height of a triangle is 8 units, the area would be:
Solution: Area of Triangle= ½×Base×Height
=½×6×8
=3×8
=24 square units.
2. Using side lengths:
If you know the lengths of all three sides of the triangle (a, b, c), you can use Heron’s formula:
Area= √S×(S-a)×(S-b)×(S-c), where S= (a +b+ c) /2.
Example: If the sides of the triangle are 7, 8, and 9 units, the area would be:
Solution: S= (7+ 8+ 9)/2 =12
Area = √12×(12-7)×(12-8)×(12-9)
=√12×5×4×3
=√720
=12√5 square units.
3. Using Trigonometry:
If you know the lengths of two sides of a triangle and one angle between those two sides, you can use trigonometry to find the area:
Area= ½×a×b×sin (C)
Where:
- a and b are the lengths of two sides of a triangle, and
- C is the angle between those two sides.
Example: If the lengths of two sides of a triangle are 5 units and 8 units respectively and the angle between them C=45° , then the area would be:
Solution: Area= ½×a×b×sin (C)
=½×5×8×sin(45°)
=½×40×1/√2
=20×1/√2
=10√2 Square units.
Area of Equilateral Triangle:
The area of an equilateral triangle with side length S can be calculated using the formula:
Area= (√3)/4×S2
Example: What is the area of an equilateral triangle whose side is equal to 6 units?
Solution: Area= (√3)/4×S2
=(√3)/4×62
=(√3)/4×36
=36√3/4
=9√3 square units.
Practice Questions:
- Find the area of the triangle with two sides as 12m and 18m and the angle between those two sides as 60°?
- Find the area of a triangle whose sides are 5 cm, 6 cm, and 9 cm?
- Find the are of a triangle whose base is 10 m and Height is 12 m?
- What is the area of an equilateral triangle whose side is equal to 8 m?
Recommended Reading
Difference between Circle and Sphere (Key Differences)
Difference between Pyramid and Prism with Examples (Key Differences)
Basic Trigonometry Formulas for Beginners in 2024- Definition, Table, all Important Formulas & FAQs.
FAQs:
1. Can the area of a triangle be negative>
Answer- No, the area of a triangle can not be negative. It represents the amount of space enclosed by the triangle and is always positive or zero.
2. How do you find the area of a triangle?
Answer- The area of a triangle can be found using various formulas, depending on the given information.
3. What information do i need to find the area of a triangle?
Answer- To find the area of a triangle, you typically need to know the lengths of the sides, the lengths of the base and height, or the lengths of two sides and the angle between them.
4. Can you find the area of any triangle if you know the lengths of all three sides?
Answer- Yes, you can find the area of any triangle if you know the lengths of all three sides using Heron’s formula.