Grade 10 · Math · Geometry

10th grade Area of a triangle without a height: sine formula and Heron's formula worksheet

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

Grade 10 Math Worksheet - Challenge Me

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

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?
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?
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?
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?
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?
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?
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?
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?
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?
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?

Area of a triangle without a height: sine formula and Heron's formula. Every version has 10 questions, and the answer key prints on the second page.

I can find the height of a triangle from a side and an angle with sine.
I can find a triangle's area as ½ × side × side × sine of the angle between them.
I can use Heron's formula when I know all three sides.

Standard: G-SRT.D.9 (+); Heron's formula has no CCSS code (G-MG.A.1 related)

height: The segment from a corner to the opposite side, meeting it square.

included angle: The angle where the two known sides meet.

sine (sin): In a right triangle: opposite side ÷ hypotenuse.

degrees mode: The calculator setting that reads angles in degrees, shown as DEG.

s (semiperimeter): Half the distance around the triangle.

Left out the ½ in a triangle's area. A triangle is half of a parallelogram with the same sides. Cut a paper parallelogram along a diagonal together.

Used cosine where sine belongs. The height is opposite the angle, so it uses sine. Label opposite, adjacent and hypotenuse together.

Used a calculator set to radians, so every sine came out wrong. Check that the calculator shows DEG before using sine.

What is the most common mistake with area of a triangle without a height: sine formula and heron's formula?

Left out the ½ in a triangle's area. A triangle is half of a parallelogram with the same sides. Cut a paper parallelogram along a diagonal together.

Are these 10th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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