Question

If each side of an isosceles triangle is 3 root 2 cm and its base is 8 cm then find the area of an isosceles triangle. ​

Answer 1

Answer:

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Answer 2

Area of the triangle will be 4√2 sq. cm.

Step-by-step explanation:

See the attached diagram.

The sides AC and BC = 3√2 cm and AB = 8 cm.

Now, draw a perpendicular on AB from vertex C which is CD and it will bisect the side AB at D.

So, AD = DB = 4 cm.

Now, from Δ CDB, applying Pythagoras Theorem,

CD² = CB² - DB² = (3√2)² - 4² = 2

⇒ CD = √2 cm

Therefore, the area of the isosceles triangle ABC will be $\frac{1}{2}\times AB \times CD = \frac{1}{2}\times 8 \times \sqrt{2} = 4\sqrt{2}$ sq. cm. (Answer)