Question

In triangle ABC, angle bisectors line AD, line BE, and line CF meet at I. If DI = 3, BD = 4, and BI = 5, then compute the area of triangle ABC

Answer 1

The area of triangle ABC is the amount of space on the triangle

The area of the triangle is 54.84 square units

How to determine the area of triangle ABC

Start by drawing the triangle (see attachment)

Next, calculate the measure of angle B using the following tangent ratio

$\tan(B/2) = \frac 34$

This gives

$\tan(B/2) = 0.75$

Take the arc tan of both sides

$B/2 = 36.87$

Multiply by 2

$B = 73.74$

Next, calculate the length of side AD using the following equation

$AD = \tan(B) * BD$

This gives

$AD = \tan(73.74) * 4$

$AD =13.71$

The area of the triangle is then calculated as:

$Area = AD * BD$

This gives

$Area = 13.71 * 4$

$Area = 54.84$

Hence, the area of the triangle is 54.84 square units

Read more about areas at:

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