In the vast realm of geometry, triangles stand as the fundamental building blocks, offering a multitude of shapes and sizes. While finding the area of a triangle is often associated with the base and height, the formulae is synonymously applicable to triangles with a 90-degree measurement to one or more of its angles. Now we get to learn of another approach of calculating the area of a triangle with three different sides and with different degrees to their angles with none measuring 90 degrees. It involves leveraging the lengths of its sides. In this blog, we will explore the intriguing method of calculating the area of a triangle using its sides, providing insights into the Heron’s Formula and its applications.
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Unlike the usual application of in working out the area of triangles, working out the area of a triangle using the three sides would command the application of the Heron’s Formula and gain a deeper understanding of geometric calculations. Through practical questions and clear explanations, Learnerscamp provides the essential resources to help you grasp the fundamentals of how to find the area of a trapezium ,how to find the area of a square ,how to find the area of a circle as well as other shapes.
Calculating Area Using Sides
Understanding Heron’s Formula:
When armed with the lengths of a triangle’s sides, Heron’s Formula becomes a powerful tool for finding its area. Named after Hero of Alexandria, this formula is particularly useful when the base and height are not readily available.
Key Formula: Heron’s Formula for Area (A)
A = √[s(s-a) (s-b) (s-c)]
Where:
- s is the semi-perimeter of the triangle, calculated as [a+b+c]/2.
- a, b, and c are the lengths of the triangle’s sides.
Step-by-Step Guide:
Let’s break down the process into manageable steps:
- Identify the Side Lengths: Start by identifying the side lengths of the triangle, marked as a, b, and c.
- Calculate the Semi-Perimeter (sp): Calculate the semi-perimeter using the formula sp= [a+b+c]/2.
- Apply Heron’s Formula: Substitute the values of s, a, b, and c into the Heron’s Formula to find the area.
- Perform the Calculation: Execute the square root and multiplication operations systematically from opening up the brackets to finally finding their roots.
- Finalize the Result: The result obtained represents the area of the triangle.
Example:
Let us find the area of a three-sided triangle with a measure of 5 cm, 6 cm and 3 cm to its sides a, b, and c.
- Find the semi-perimeter s = (a + b + c)/2 which is = (5 + 6 + 3)/2 = 7
- To calculate the area, apply Heron’s formula to your found answer above
A = √[s(s-a) (s-b) (s-c)]
Area= √[7(7-5)(7-6)(7-3)]
A= √[7 × 2 × 1 × 4]
= √(56)
≈ 7.48
Real-world Applications:
Heron’s Formula finds application in various scenarios:
- Surveying: Surveyors use Heron’s Formula for irregularly shaped plots where traditional methods may be impractical.
- Architecture: Architects employ this formula when working with triangles formed by non-linear structures.
Embark on a geometric adventure as we unveil the mysteries of calculating the area of a triangle using its sides. Heron’s Formula, with its elegance and precision, becomes our guide in this journey.
So, the next time you encounter a triangle with known side lengths, remember that the area of a triangle is within your grasp through the marvels of Heron’s Formula.
Point to note: the Heron’s Formula can be applied to the calculation of the area of all types of triangles given the measure of the sides are available or known to the student.
