Question

find the area of the following figure:

$\Delta$ were side a = 12cm, side b = 12 cm and the base is 8cm

Answer 1

Let ABC be the triangle with AB = 12 cm AC = 12 cm and BC = 8 cm Since AB = AC, Triangle is isosceles. So, by property of isosceles triangles the altitude will based the base. Now in Delta ADC AD = h DC = 8/2 = 4 cm. AC = 12 cm. By Pythagoras's theorem AD^2 + DC^2 = AC^2 h^2 + (4)^2 = (12)^2 h^2 = 144 - 16 h^2 = 128 h = squareroot 128 Area of Delta = 1/2 times base times height = 1/2 times 8 times squareroot 128 = 4 squareroot 128 = 32 squareroot 2 cm^2