Worksheet

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

Grade 10 Math Worksheet - Building Confidence

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

  1. Milo's sail is triangle FGH with FG = 12 cm and angle G = 40°. The height FD meets GH at a right angle. To the nearest tenth, how long is FD, in centimeters?

  2. Noah's pizza slice is triangle FGH with FG = 9 in and angle G = 20°. The height FD meets GH at a right angle. To the nearest tenth, how long is FD, in inches?

  3. Pia's tent side is triangle FGH with FG = 13 ft and angle G = 77°. The height FD meets GH at a right angle. To the nearest tenth, how long is FD, in feet?

  4. Tala's paper flag is triangle FGH with FG = 14 cm and angle G = 58°. The height FD meets GH at a right angle. To the nearest tenth, how long is FD, in centimeters?

  5. Zee's sandwich half is triangle FGH with FG = 7 cm, GH = 12 cm, angle G = 80° and angle H = 33°. Which expression gives its area?

    • ½ × 7 × 12 × sin 33°
    • ½ × 7 × 12 × sin 80°
    • ½ × 7 × 12
    • 7 × 12 × sin 80°

  6. Ari's pennant is triangle FGH with FG = 9 in, GH = 13 in, angle G = 70° and angle H = 40°. Which expression gives its area?

    • ½ × 9 × 13 × sin 40°
    • 9 × 13 × sin 70°
    • ½ × 9 × 13
    • ½ × 9 × 13 × sin 70°

  7. Esme's park lawn is triangle FGH with FG = 12 m, GH = 9 m, angle G = 35° and angle H = 97°. Which expression gives its area?

    • 12 × 9 × sin 35°
    • ½ × 12 × 9 × sin 35°
    • ½ × 12 × 9 × sin 97°
    • ½ × 12 × 9

  8. Jun's sail is triangle FGH with FG = 9 cm and GH = 14 cm. Its height FD is 6.9 cm. To the nearest tenth, what is its area, in square centimeters?

  9. Luz's tent door is triangle FGH with FG = 7 ft and GH = 12 ft. Its height FD is 6.2 ft. To the nearest tenth, what is its area, in square feet?

  10. Milo's picnic lawn is triangle FGH with FG = 13 m and GH = 20 m. Its height FD is 9 m. To the nearest tenth, what is its area, in square meters?

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

Answer Key - Grade 10 Math Worksheet - Building Confidence

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

  1. Milo's sail is triangle FGH with FG = 12 cm and angle G = 40°. The height FD meets GH at a right angle. To the nearest tenth, how long is FD, in centimeters?

    7.7

  2. Noah's pizza slice is triangle FGH with FG = 9 in and angle G = 20°. The height FD meets GH at a right angle. To the nearest tenth, how long is FD, in inches?

    3.1

  3. Pia's tent side is triangle FGH with FG = 13 ft and angle G = 77°. The height FD meets GH at a right angle. To the nearest tenth, how long is FD, in feet?

    12.7

  4. Tala's paper flag is triangle FGH with FG = 14 cm and angle G = 58°. The height FD meets GH at a right angle. To the nearest tenth, how long is FD, in centimeters?

    11.9

  5. Zee's sandwich half is triangle FGH with FG = 7 cm, GH = 12 cm, angle G = 80° and angle H = 33°. Which expression gives its area?

    • ½ × 7 × 12 × sin 33°
    • ½ × 7 × 12 × sin 80°
    • ½ × 7 × 12
    • 7 × 12 × sin 80°

  6. Ari's pennant is triangle FGH with FG = 9 in, GH = 13 in, angle G = 70° and angle H = 40°. Which expression gives its area?

    • ½ × 9 × 13 × sin 40°
    • 9 × 13 × sin 70°
    • ½ × 9 × 13
    • ½ × 9 × 13 × sin 70°

  7. Esme's park lawn is triangle FGH with FG = 12 m, GH = 9 m, angle G = 35° and angle H = 97°. Which expression gives its area?

    • 12 × 9 × sin 35°
    • ½ × 12 × 9 × sin 35°
    • ½ × 12 × 9 × sin 97°
    • ½ × 12 × 9

  8. Jun's sail is triangle FGH with FG = 9 cm and GH = 14 cm. Its height FD is 6.9 cm. To the nearest tenth, what is its area, in square centimeters?

    48.3

  9. Luz's tent door is triangle FGH with FG = 7 ft and GH = 12 ft. Its height FD is 6.2 ft. To the nearest tenth, what is its area, in square feet?

    37.2

  10. Milo's picnic lawn is triangle FGH with FG = 13 m and GH = 20 m. Its height FD is 9 m. To the nearest tenth, what is its area, in square meters?

    90