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Area of triangles: 1/2 a*b sin(C)

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Intros
Lessons
  1. Introduction to Area of Triangles: 12absin⁡C\frac{1}{2} ab\sin C
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Examples
Lessons
  1. Proof: Area of Triangle = 12absin⁡C\frac{1}{2} ab\sin C

    Using the given diagram, prove that the area of a triangle can be found by the equation 12absin⁡C\frac{1}{2} ab\sin C

    MATH11 10 10 1
    1. Finding the Area of a Triangle Given 2 Sides and the Angle in Between

      ΔXYZ\Delta XYZ has side lengths XYXY=9cm, XZXZ=12cm and ∠YXZ\angle YXZ=42°. Find the area of ΔXYZ\Delta XYZ. Give your answer to 1 decimal place.

      1. Area of Isosceles Triangles

        The area of an isosceles triangle ΔABC\Delta ABC is 42.25 cm2cm^{2}. If ∠A\angle A=30°, find the length of ABAB in exact value.

        MATH11 10 10 3
        1. Area of Equilateral Triangles

          An equilateral triangle has side length 4cm. Find its area and give your answer in exact value.

          1. Determining the Areas of Different Triangles

            Find the area of the following triangle.

            MATH11 10 10 5

            1. Find the area of the following right-angled triangle.

              MATH11 10 10 6
              Topic Notes
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              In this lesson, we will learn:
              • Proof: Area of Triangle =12absin⁡C\frac{1}{2}ab \sin C
              • Finding the Area of a Triangle Given 2 Sides and the Angle in Between
              • Area of Isosceles Triangles
              • Area of Equilateral Triangles
              • Determining the Areas of Different Triangles

              Notes:
              • The base and height of a triangle must be perpendicular to each other.
              • The traditional formula for the area of a triangle = 12×base×height\frac{1}{2} \times base \times height
              • An isosceles triangle has two sides of equal length.
              • An equilateral triangle has three sides of equal length and all the inner angles equal to 60°.
              • Angles inside a triangle add up to 180°.
              • Pythagorean Theorem: a2+b2=c2a^{2}+b^{2}=c^{2}