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

NameDate

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

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?
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?
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?
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?
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?
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?
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?
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?
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?
Milo's park lawn is triangle FGH with FG = 10 m, GH = 14 m and angle G = 60°. What is its area in square meters, as a simplified radical?

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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