How to find the area of an acute / obtuse triangle - ACT Math

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Question

The base of a triangle is $8\ cm$ and the area is $48\ cm^2$ . The height of the triangle is then decreased by . What is the final area of the triangle?

Answer

The formula for the area of a triangle is

$\frac{1}{2}b \times h$ .

If the area is equal to 48 cm2 and the base is 8 cm, then the initial height is:

$48 = \frac{1}{2} \times 8 \times h$

If 12 is decreased by 75% then

$12 \times .75 = 9$ , and . The final height is 3 cm.

Therefore the final area is

$\frac{1}{2}\times 8\times 3=12$ .

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