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nikdorinn [45]
3 years ago
12

Work out the area of triangle ABC.

Mathematics
2 answers:
SVETLANKA909090 [29]3 years ago
6 0

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

Savatey [412]3 years ago
6 0

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}

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