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

Answer Key - Grade 10 Math Worksheet - Challenge Me

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

1. 1.

   Noah's garden is triangle FGH with an area of 60 square meters, FG = 10 m and angle G = 40°. To the nearest tenth, how long is GH, in meters?

   18.7
2. 2.

   Pia's tent side is triangle FGH with an area of 45 square feet, FG = 9 ft and angle G = 55°. To the nearest tenth, how long is GH, in feet?

   12.2
3. 3.

   Ren's sail is triangle FGH with an area of 84 square inches, FG = 12 in and angle G = 120°. To the nearest tenth, how long is GH, in inches?

   16.2
4. 4.

   Tala's paper flag is triangle FGH with an area of 36 square centimeters, FG = 8 cm and angle G = 72°. To the nearest tenth, how long is GH, in centimeters?

   9.5
5. 5.

   Zee's patio is parallelogram FGHQ with FG = 9 ft, GH = 14 ft and angle G = 65°. To the nearest tenth, what is its area, in square feet?

   114.2
6. 6.

   Ari's tile is parallelogram FGHQ with FG = 12 cm, GH = 15 cm and angle G = 128°. To the nearest tenth, what is its area, in square centimeters?

   141.8
7. 7.

   Esme's rug is parallelogram FGHQ with FG = 8 in, GH = 20 in and angle G = 108°. To the nearest tenth, what is its area, in square inches?

   152.2
8. 8.

   Jun's park lawn is a triangle with sides of 11 m, 13 m and 20 m. No angle is known. Using Heron's formula, what is its area, in square meters?

   66
9. 9.

   Kira's garden bed is a triangle with sides of 7 ft, 15 ft and 20 ft. No angle is known. Using Heron's formula, what is its area, in square feet?

   42
10. 10.

    Milo's pennant is a triangle with sides of 10 in, 13 in and 13 in. No angle is known. Using Heron's formula, what is its area, in square inches?

    60