Question

In an isosceles triangle, the measure of each of equal sides is 10 cm and the angle between them is 45º. The area of the triangle is:

(a) 25 cm² 

(b) \(\frac{25}{2}\sqrt2\) cm² 

(c) 25 √2 cm² 

(d) 25 √3 cm²

Answer 1

(c) 25√2 cm².

ΔABC is an isosceles triangle with AB = AC = 10 cm. ∠A = 45° 

∴ Area of ΔABC

= \(\frac{1}{2}\) x 10 x 10 x sin 45°

[Using Δ = \(\frac{1}{2}\) bc sin A]

= \(\frac{50}{\sqrt2}\) = \(\frac{50}{\sqrt2}\) x \(\frac{\sqrt2}{\sqrt2}\) = 25√2 cm².