Question

∆ABC is isosceles with AB = AC = 6 cm, BC = 8 cm. The height AD from A
to BC is 7 cm. Find the area of ∆ABC. What will be the height from C on AB?

Answer 1

it is the area of triangle ( by right angle property )

Answer 2

Given:

∆ ABC is isosceles triangle

AB = AC = 6 cm, BC = 8 cm

AD = 7 cm.

To Find:

The area of ∆ABC

The height from C on AB

Solution:

we know,

Area of right-angle triangle = 1/2 * b * h

Area of ∆ ABC = Area of ∆ ABD + Area of ∆ ACD

now,

BC = BD + DC

BD = BC = 4cm

Area of ∆ ADC = 1/2 * DC * AD

Area of ∆ ADC = 1/2 * 4 * 7 = 14 cm²

Similarly,

Area of ∆ ADB = 1/2 * BD * AD

Area of ∆ ADB = 1/2 * 4 * 7 = 14cm²

∴ Area of ∆ ABC = 14 + 14 = 28cm²

So, the Area of ∆ ABC = 28cm² and height from C on AB is 7cm.