See the attached image. In that diagram, I'm focusing on triangle ABC which is one of the lateral sides. I've added h to the diagram which is the unknown slant height along the dashed line. I've also added point F which is directly under point A and also on segment BC.
Triangle AFC is a 30-60-90 triangle Side FA = h is the unknown longer leg The known shorter leg is FC = 7 since it is half of CB = 14
By using the 30-60-90 triangle template, we know that longer leg = (shorter leg)*sqrt(3) longer leg = 7*sqrt(3) FA = 7*sqrt(3) h = 7*sqrt(3)
Which means the area of triangle ABC is area = (base*height)/2 area = (FC*FA)/2 area = (7*h)/2 area = (7*7*sqrt(3))/2 area = (49*sqrt(3))/2 that is the area of one triangle. But there are four of these triangles, so we multiply that result by 4
4*area = 4*(49*sqrt(3))/2 = 98*sqrt(3) which is the answer
note: the base is the square BCDE. The lateral sides are everything that isn't the base (so all of the triangles)
