Question

Work out the area of triangle ABC.

Answer 1

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√(2)}+\stackrel{DC}{√(2)}\\ \qquad 4√(2) \\h=√(2) \end{cases}\implies \begin{array}{llll} A=\cfrac{1}{2}(4√(2))(√(2))\implies A=2(√(2))^2\\\\ A=2√(2^2)\implies A=2\cdot 2\implies A=4 \end{array}`

Answer 2

4 cm²

Explanation:

Area = ½.bh

b = base (cm²)

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

`h^(2) = (2 √(5) )^(2) - (3 √(2) )^(2) \\ {h}^(2) = 20 - 18 \\ {h}^(2) = 2 \\ h \: = √(2)`

`b \: = 3√(2) + √(2) \\ b \: = 4 √(2)`

`Area \: = (1)/(2) .(4 √(2) )( √(2) ) \\ Area \: =4`