Question

The sides of a $\Delta$ $ABC$ measure $6$ cm, $8$ cm and $10$ cm. The area of the triangle is __________.

• A. $40{\text{cm}}^2$
• B. $24{\text{cm}}^2$
• C. $30{\text{cm}}^2$
• D. None of these

Answer 1

The correct option is B $24{\text{cm}}^2$

Given, sides of a triangle $\Delta ABC$ are $6$ cm, $8$ cm, $10$ cm

Given sides are sides of right angled triangle

Hypotenuse $=10$ cm

Now applying pythagorous theorem

$h^2=B^2+P^2$

${10}^2=6^2+8^2$

$100=36+64=100$

Hence, proved.

Area of triangle $=\Delta =\frac{1}{2}\times \left(\text{base}\right)\left(\text{height}\right)$

$\Delta =\frac{1}{2}\times \left(6\text{cm}\right)\left(8\text{cm}\right)$

$\Delta =24{\text{cm}}^2$