In triangle PQR, PQ=6 cm, PR=8 cm, and QR=12 cm. Calculate the area of the…
2024
In triangle PQR, PQ=6 cm, PR=8 cm, and QR=12 cm. Calculate the area of the triangle PQR
- A.
23.33 cm^2
- B.
17.5 cm^2
- C.
21.33 cm^2
- D.
28.67 cm^2
Attempted by 4 students.
Show answer & explanation
Correct answer: C
Solution:
Step 1 — Check that the side lengths form a valid triangle: 6 + 8 > 12, 6 + 12 > 8, and 8 + 12 > 6, so a triangle is possible.
Step 2 — Use Heron's formula. Compute the semiperimeter:
s = (6 + 8 + 12) / 2 = 13
Compute the three differences: s − 6 = 7, s − 8 = 5, s − 12 = 1
Area = sqrt[s·(s − 6)·(s − 8)·(s − 12)] = sqrt[13 · 7 · 5 · 1] = sqrt(455) ≈ 21.3307...
Final answer: The area of triangle PQR is approximately 21.33 cm^2 (rounded to two decimal places).