 Hello and welcome to the session. In this session we shall discuss the following question and the question says that, find the area of an equilateral triangle with height 4 cm. Let us start with the solution of the given question. Here we have to find the area of an equilateral triangle having height 4 cm. To solve it we will use the strategy of drawing. So we shall first draw an equilateral triangle A, B, C. It is given that its height is 4 cm. So from vertex A we draw a perpendicular to the base B, C, meeting B, C at point D. So A, D is 4 cm. Also angle D is 90 degrees. Now we have to find its area. We know that area of triangle is equal to 1 by 2 into base into height. Here we know the height and now we have to find its base. So first we find its base and then its area. Since it is an equilateral triangle so length of all sides is equal. So we'll let length of each side of triangle A, B, C be x cm. That is A, B is equal to B, C is equal to C, A is equal to x cm. Also A, D by 6 BC which means B, D is equal to DC and that is equal to x by 2 cm. So here we have A, B is equal to x, AC is equal to x, BC is equal to x and BD is equal to x by 2 and DC is equal to x by 2. Now here we see that triangle A, BC is a right angle triangle. So using Pythagoras theorem we have A, D square plus C, D square is equal to AC square. Now substituting the values of A, D, C, D and AC here we get 4 square plus x by 2 whole square is equal to x square. This implies 16 plus x square by 4 is equal to x square which further implies that 16 is equal to x square minus x square upon 4 which implies 16 is equal to now taking LCM here we get 4 in the denominator and in the numerator we have 4x square minus x square which implies that 16 is equal to 3x square upon 4. Now this implies that x square is equal to 16 into 4 whole upon 3 that is x square is equal to 64 upon 3. Now taking positive square root on both sides we get x is equal to square root of 64 by 3 which implies that x is equal to 8 upon square root of 3. So base BC which is equal to x will be equal to 8 upon square root of 3 centimeters. So area of triangle ABC that is equal to half into base into height will be equal to 1 by 2 into base that is 8 upon square root of 3 into height that is 4. Now this is equal to 16 upon square root of 3 centimeters square thus we say that area of triangle ABC is equal to 16 upon square root of 3 centimeters square which is the required answer. This completes our session. Hope you enjoyed this session.