Triangle Area with Half ab sin C · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.
به انگلیسی

Half, times, times sine

Mathematics · Geometry · ages 15-16
Name ______________________   Date ____________

  1. Triangle ABC has sides AB, BC, and CA. You want the area using angle B. Which two sides go with sin B?

    • BC and CA
    • AB and CA
    • AB and BC
    • All three sides

  2. Two sides of a triangle are 9 cm and 12 cm, with a 30 degree angle between them. What is the area?

    • 27 cm squared
    • 54 cm squared
    • 108 cm squared
    • 13.5 cm squared

  3. Triangle PQR has sides PQ, QR, and PR. You want the area using angle Q. Which two sides go with sin Q?

    • PQ and QR
    • QR and PR
    • PQ and PR

  4. An internal diagonal splits a quadrilateral into triangles of area 14 cm squared and 9 cm squared. What is the total area, in cm squared?

    Answer: ______________

  5. Two sides are 5 cm and 8 cm and the area is 10 cm squared. What is the acute angle between those sides, in degrees?

    Answer: ______________

  6. Two sides of a triangle are 5 cm and 8 cm, and the area is 10 cm squared. What is the acute angle between those two sides, in degrees?

    Answer: ______________

  7. Two sides of a triangle are 10 cm and 7 cm, with a 30 degree angle between them. What is the area, in cm squared?

    Answer: ______________

  8. Two sides are 12 cm and 5 cm with a 30 degree angle between them. What is the area, in cm squared?

    Answer: ______________

  9. Two sides of a triangle are both 8 cm, and the area is 16 cm squared. What is the smaller of the two possible angles between them, in degrees?

    Answer: ______________

  10. Two sides are both 10 cm and the area is 25 cm squared. What is the smaller of the two possible angles between them?

    • 150 degrees
    • 90 degrees
    • 30 degrees
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Half, times, times sine W1-mt_PiwizT4D2b-s1

  1. AB and BC · Angle B sits between AB and BC, so those two belong in the formula.
  2. 27 cm squared · One half times 9 times 12 times sin 30 is 54 times 0.5, which is 27.
  3. PQ and QR · Angle Q sits between PQ and QR, so those two belong in the formula.
  4. 23 · Add the two triangle areas: 14 plus 9 is 23.
  5. 30 · Sin C equals 20 over 40, which is 0.5, and inverse sine gives 30.
  6. 30 · Sin C equals 20 over 40, which is 0.5, and the acute inverse sine gives 30.
  7. 17.5 · One half times 10 times 7 times sin 30 is 35 times 0.5, which is 17.5.
  8. 15 · One half times 12 times 5 times sin 30 is 30 times 0.5.
  9. 30 · Sin C equals 32 over 64, which is 0.5. The candidates are 30 and 150 degrees, and the smaller is 30.
  10. 30 degrees · Sin C is 0.5, shared by 30 and 150, and the smaller is 30.
Worksheet · LightMySky