Question

Work out the area of triangle ABC.

Answer 1

Answer:

A = 4 cm²

Step-by-step explanation:

The area of a triangle is calculated as

A = $\frac{1}{2}$ bh ( b is the base and h the perpendicular height )

b = AC = 3$\sqrt{2}$ + $\sqrt{2}$ = 4$\sqrt{2}$

h = BD

Calculate BD using Pythagoras' identity in Δ ABD

BD² = AB² - AD²

      = (2$\sqrt{5}$ )² - (3$\sqrt{2}$ )²

     = 20 - 18 = 2 ( take square root of both sides )

BD = $\sqrt{2}$

Then

A = $\frac{1}{2}$ × 4$\sqrt{2}$ × $\sqrt{2}$ = 2 × $\sqrt{2}$ × $\sqrt{2}$ = 4 cm²