2021-12-16

Triangle divided in three areas | Find middle area

This question was uploaded on 15/12/21 on social media accounts.

Solution:

By heron's formula, area of the triangle is 84.
\[\Rightarrow \frac12(10)(21)\sin\theta = 84\]
Let sinθ/2 = A:
\[\Rightarrow A = \frac25\]
Now,
\[A_1 = (4)(5)A = 8\]
\[A_1+A_2 = (8)(15)A = 48\]
Blue Area:
\[A_2 = 48-8 = 40\]
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