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

Name Date

Area of a triangle Problem set B

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

Each question matches the question with the same number in set A. Do the ones you got wrong there.

Difficulty: first skills applying them stretch

Skills

  1. In triangle DEF, DE = 7.9 cm, FD = 10.3 cm and angle D = 49°. Find the area of the triangle.

    10.3 cm7.9 cm49°DEF

  2. In triangle KLM, KL = 7.4 cm, LM = 9.1 cm and angle KLM = 115°. Find the area of the triangle.

    9.1 cm7.4 cm115°LKM

  3. Triangle XYZ has XY = 9.6 cm, ZX = 6.8 cm and area 27.3 cm². Angle X is acute. Find angle X.

    6.8 cm9.6 cmθXYZ

  4. Triangle PQR has PQ = 8.0 cm, angle P = 42° and area 36 cm². Find the length of RP.

    x8.0 cm42°PQR

  5. In triangle DEF, EF = 8.3 cm, FD = 6.1 cm and DE = 11.5 cm. Find the smallest angle.

    8.3 cm6.1 cm11.5 cmθDEF

  6. In triangle XYZ, the perpendicular from Y meets XZ at S and YS = h. The sides are x = YZ and y = ZX. Show that the area of the triangle is \(\frac12 xy\sin Z\).

    xyhZZXYS

In context

  1. A triangular flower bed has two sides of 6.2 m and 5.1 m. The angle between them is 66°. Find the area of the flower bed.

    5.1 m6.2 m66°FGH

  2. A triangular garden bed LMN has area 9.2 m². LM = 4.6 m and angle L = 47°. Find the length of NL.

    x4.6 m47°LMN

  3. A triangular car park has sides of 48 m, 71 m and 90 m.

    48 m71 m90 mθDEF
    1. (a) Find the largest angle of the car park.
    2. (b) Find the area of the car park.

Stretch

  1. Triangle DEF has DE = 5.5 cm, FD = 8.0 cm and area 18 cm². Find the two possible sizes of angle D.

    8.0 cm5.5 cmDEF

  2. A paving slab WXYZ has sides WX = 6.4 m, XY = 8.2 m, YZ = 7.9 m and ZW = 7.0 m. Angle WXY = 72°.

    6.4 m8.2 m7.9 m7.0 m72°θWXYZ
    1. (a) Find the area of triangle WXY.
    2. (b) Find the length of WY.
    3. (c) Find angle WZY.
    4. (d) Find the area of the quadrilateral WXYZ.

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