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.

   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
2. 2.

   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
3. 3.

   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
4. 4.

   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
5. 5.

   Bo's garden plot is parallelogram FGHQ with FG = 7 m, GH = 11 m and angle G = 45°. To the nearest tenth, what is its area, in square meters?

   54.4
6. 6.

   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
7. 7.

   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
8. 8.

   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
9. 9.

   Luz's playground is a triangle with sides of 13 m, 20 m and 21 m. No angle is known. Using Heron's formula, what is its area, in square meters?

   126
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