In triangle ABC the side BC is 12 cm long. The triangle is obtuse, so the foot of the perpendicular from A to the line BC falls outside the segment BC — 4 cm beyond B — and that perpendicular is 5 cm long. Find the area of the triangle in cm².

Question

Accepted Answer

30. Area = ½ × base × height, and the base is the side BC itself, 12 cm, whatever the height's foot does. Area = ½ × 12 × 5 = 30 cm². (Stretching the base to 12 + 4 = 16 cm gives 40 cm², but the extra 4 cm is not part of the triangle; shrinking it to 12 − 4 = 8 cm gives 20 cm²; 60 cm² drops the ½.)

In triangle ABC the side BC is 12 cm long. The triangle is obtuse, so the foot of the perpendicular from A to the line BC falls outside the segment BC — 4 cm beyond B — and that perpendicular is 5 cm long. Find the area of the triangle in $cm^{2}$ .

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More Areas & Volumes practice

In triangle ABC the side BC is 12 cm long. The triangle is obtuse, so the foot of the perpendicular from A to the line BC falls outside the segment BC — 4 cm beyond B — and that perpendicular is 5 cm long. Find the area of the triangle in cm2.

Step-by-Step Solution

Master this topic in 30 minutes a day.

More Areas & Volumes practice

In triangle ABC the side BC is 12 cm long. The triangle is obtuse, so the foot of the perpendicular from A to the line BC falls outside the segment BC — 4 cm beyond B — and that perpendicular is 5 cm long. Find the area of the triangle in $cm^{2}$ .