Question

Work out the area of triangle ABC.

Answer 1

Answer:

4 cm²

Step-by-step explanation:

Area = ½.bh

b = base (cm²)

h = perpendicular height, i.e. BD (cm²)

$h^{2} = (2 \sqrt{5} )^{2} - (3 \sqrt{2} )^{2} \\ {h}^{2} = 20 - 18 \\ {h}^{2} = 2 \\ h \: = \sqrt{2}$

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

$Area \: = \frac{1}{2} .(4 \sqrt{2} )( \sqrt{2} ) \\ Area \: =4$

Answer 2

Check the picture below.

so we know the triangle has an altitude/height of √2, then

$\textit{area of a triangle}\\\\ A=\cfrac{1}{2}bh~~ \begin{cases} b=base\\ h=height\\[-0.5em] \hrulefill\\ b=\stackrel{AD}{3\sqrt{2}}+\stackrel{DC}{\sqrt{2}}\\ \qquad 4\sqrt{2} \\h=\sqrt{2} \end{cases}\implies \begin{array}{llll} A=\cfrac{1}{2}(4\sqrt{2})(\sqrt{2})\implies A=2(\sqrt{2})^2\\\\ A=2\sqrt{2^2}\implies A=2\cdot 2\implies A=4 \end{array}$