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IB Mathematics: Applications and Interpretation HL · 12.10: Geometry & Trigonometry · 12.10.3

Name Date

Area of a triangle Problem set A

Say which angle is between the two sides. Give areas, lengths and angles to 3 significant figures, with units (cm², m²).

Difficulty: first skills applying them stretch

Skills

  1. In triangle ABC, AB = 12.4 cm, CA = 8.7 cm and angle A = 57°. Find the area of the triangle.

    8.7 cm12.4 cm57°ABC

  2. In triangle PQR, PQ = 6.3 cm, QR = 10.8 cm and angle PQR = 128°. Find the area of the triangle.

    10.8 cm6.3 cm128°QPR

  3. Triangle ABC has AB = 11.2 cm, CA = 7.4 cm and area 31.5 cm². Angle A is acute. Find angle A.

    7.4 cm11.2 cmθABC

  4. Triangle ABC has AB = 10.0 cm, angle A = 55° and area 48 cm². Find the length of CA.

    x10.0 cm55°ABC

  5. In triangle ABC, BC = 7.6 cm, CA = 9.4 cm and AB = 13.2 cm. Find the smallest angle.

    7.6 cm9.4 cm13.2 cmθABC

  6. In triangle PQR, the perpendicular from Q meets PR at S and QS = h. The sides are p = QR and q = RP. Show that the area of the triangle is \(\frac12 pq\sin R\).

    pqhRRPQS

In context

  1. A triangular sail has two edges of 4.8 m and 3.9 m. The angle between them is 72°. Find the area of the sail.

    3.9 m4.8 m72°STU

  2. A triangular roof panel RST has area 7.5 m². RS = 3.4 m and angle R = 58°. Find the length of TR.

    x3.4 m58°RST

  3. A triangular plot of land has sides of 62 m, 85 m and 104 m.

    62 m85 m104 mθABC
    1. (a) Find the largest angle of the plot.
    2. (b) Find the area of the plot.

Stretch

  1. Triangle ABC has AB = 9.0 cm, CA = 7.0 cm and area 24 cm². Find the two possible sizes of angle A.

    7.0 cm9.0 cmABC

  2. In the quadrilateral ABCD, AB = 7.3 cm, BC = 9.6 cm, CD = 8.8 cm, DA = 6.1 cm and angle ABC = 64°.

    7.3 cm9.6 cm8.8 cm6.1 cm64°θABCD
    1. (a) Find the area of triangle ABC.
    2. (b) Find the length of AC.
    3. (c) Find angle ADC.
    4. (d) Find the area of the quadrilateral ABCD.

jmaths.xyz · AI HL · 12.10.3 Area of a triangle