Question

ABCD is a square of side 4 cm. If E is a point in the interior of the square such that ΔCED is equilateral, then area of Δ ACE is

(a) $2\sqrt{3}-1c{m}^2$

(b) $4\sqrt{3}-1c{m}^2$

(c) $6\sqrt{3}-1c{m}^2$

(d) $8\sqrt{3}-1c{m}^2$

Answer 1

We have the following diagram.

Since is equilateral,

Therefore,

Now,

Since AC is diagonal of sqr.ABCD

Therefore,

Therefore we get,

Now, in , draw a perpendicular EM to the base AC.

So in ,

Therefore,

Now in ,

So the answer is (b)