Question

What is the area of a triangle having sides 6 cm, 8 cm and 10 cm ?

• A. 8 cm²
• B. 10 cm²
• C. 24 cm²
• D. 14 cm²

Answer 1

Answer:

C. 24 cm²

To find the area of a triangle with side lengths 6 cm, 8 cm, and 10 cm, we can first check if it forms a right-angled triangle using the Pythagorean theorem ($a^2 + b^2 = c^2$):

$6^2 + 8^2 = 36 + 64 = 100$
$10^2 = 100$

Since $6^2 + 8^2 = 10^2$, this is a right-angled triangle where:

• Base = 6 cm

• Height = 8 cm

• Hypotenuse = 10 cm

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Area Calculation

The formula for the area of a right-angled triangle is:
$\text{Area} = \frac{1}{2} \times \text{Base} \times \text{Height}$

Substitute the values into the formula:
$\text{Area} = \frac{1}{2} \times 6 \times 8$
$\text{Area} = 3 \times 8 = \mathbf{24\text{ cm}^2}$

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Final Answer

The area of the triangle is 24 cm².