Area of a triangle without a height: sine formula and Heron's formula

Answer Key - Grade 10 Math Worksheet

Circle the best answer, or write your answer on the line.

1. 1.

   Noah's sail is triangle FGH with FG = 9 cm, GH = 14 cm, angle G = 52° and angle H = 40°. To the nearest tenth, what is its area, in square centimeters?

   49.6
2. 2.

   Pia's tent side is triangle FGH with FG = 11 ft, GH = 15 ft, angle G = 40° and angle H = 47°. To the nearest tenth, what is its area, in square feet?

   53
3. 3.

   Tala's park lawn is triangle FGH with FG = 10 m, GH = 16 m, angle G = 115° and angle H = 24°. To the nearest tenth, what is its area, in square meters?

   72.5
4. 4.

   Zee's garden bed is triangle FGH with FG = 6 ft, GH = 13 ft, angle G = 130° and angle H = 15°. To the nearest tenth, what is its area, in square feet?

   29.9
5. 5.

   Ari's pennant is triangle FGH with FG = 8 in, GH = 18 in, angle G = 28° and angle H = 19°. To the nearest tenth, what is its area, in square inches?

   33.8
6. 6.

   Bo's garden is triangle FGH with FG = 6 m, GH = 10 m and angle G = 60°. What is its area in square meters, as a simplified radical?

   15√3
7. 7.

   Esme's sail is triangle FGH with FG = 8 ft, GH = 12 ft and angle G = 60°. What is its area in square feet, as a simplified radical?

   24√3
8. 8.

   Jun's ramp side is triangle FGH with FG = 4 ft, GH = 14 ft and angle G = 120°. What is its area in square feet, as a simplified radical?

   14√3
9. 9.

   Kira's pennant is triangle FGH with FG = 8 in, GH = 10 in and angle G = 45°. What is its area in square inches, as a simplified radical?

   20√2
10. 10.

    Luz's sandwich half is triangle FGH with FG = 6 cm, GH = 12 cm and angle G = 135°. What is its area in square centimeters, as a simplified radical?

    18√2