Question-181221

Question Number 181221 by cortano1 last updated on 23/Nov/22

Answered by mr W last updated on 23/Nov/22

Commented by cortano1 last updated on 23/Nov/22

nicesolution

Commented by mr W last updated on 23/Nov/22

Δ G E A \equiv Δ C E D

\Rightarrow [A B C D] = [Δ G B C]

C B = 34 + 8.5 = 42.5

C G = 2 \times 16 = 32

\cos α = \frac{16^{2} + 34^{2} - 30^{2}}{2 \times 16 \times 34} = \frac{8}{17}

\Rightarrow \sin α = \sqrt{1 - {(\frac{8}{17})}^{2}} = \frac{15}{17}

[Δ G B C] = \frac{C G \times C B \times \sin α}{2}

= \frac{32 \times 42.5 \times 15}{2 \times 17} = 600

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