ABCD is a squared of side 4 cm . If E is a point in the interior of the square such that ΔCED is equilateral, then find area of ΔACE (incm 2 )

Sure, here is the step by step solution:

Step 1: We know that all angles in an equilateral triangle are 60 degrees. Therefore, ∠CED = 60°.

Step 2: Since ABCD is a square, ∠CAB = 90°. Therefore, ∠EAC = 90° - 60° = 30°.

Step 3: In triangle ACE, ∠ACE = 180° - 90° - 30° = 60°. So, triangle ACE is a 30-60-90 triangle.

Step 4: In a 30-60-90 triangle, the sides are in the ratio 1:√3:2. Since AC is the hypotenuse of triangle ACE and is 4 cm (the side of the square), AE = AC/2 = 2 cm and CE = AC*√3/2 = 2√3 cm.

Step 5: The area of a triangle is 1/2 * base * height. Here, base AE = 2 cm and height CE = 2√3 cm. Therefore, the area of triangle ACE = 1/2 * 2 cm * 2√3 cm = 2√3 cm².