Question
Download Solution PDFThe three sides of a triangle are 7 cm, 9 cm and 8 cm. What is the area of the triangle?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Length of the three sides of the triangle: 7 cm, 9 cm, and 8 cm
Formula used:
To find the area of a triangle when the lengths of all three sides are known, we can use Heron's formula:
Area = √(s(s - a)(s - b)(s - c))
Where:
s = (a + b + c)/2 (semi-perimeter of the triangle)
a, b, c = lengths of the three sides
Calculation:
Using the formula:
s = (a + b + c)/2
s = (7 + 9 + 8)/2
s = 24/2
s = 12 cm
Now, plug the values of a, b, c, and s into Heron's formula to find the area of the triangle:
√(s(s - a)(s - b)(s - c))
√(12(12 - 7)(12 - 9)(12 - 8))
√(12 × 5 × 3 × 4)
12√5 Sq. cm
Therefore, the area of the triangle with side lengths 7 cm, 9 cm, and 8 cm is approximately 12√5 Sq. cm
Last updated on Jul 22, 2025
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