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Question

What is the area formula of an obtuse triangle?


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Solution

Determine the area formula of an obtuse triangle.

An obtuse triangle is a triangle whose one angle is obtuse that is greater than 90°.

Consider a triangle ABC where ACB is an obtuse angle

As it can be seen, the Area of ABC is equals a difference between the area of ΔABDandΔACD.

Since, Areaofrightangletriangle=12×base×height

Now
Area of ABD

SABD=12×BD×h

And

Area of ACD

SACD=12×CD×h
Calculate the difference of the above equation:

SABC=SABD-SACD=12×BD×h12×CD×h=12×(BDCD)×h=12×a×h

Where a is the base of the ABC and h is the height perpendicular to extended a ABC
Hence, the area formula of an obtuse triangle is “12×base×height”.


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