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Calculate the area of this triangle - OCR - GCSE Maths - Question 18 - 2018 - Paper 1

Question 18

Calculate the area of this triangle. 5.8 cm 3.9 cm 6.4 cm Not to scale

Worked Solution & Example Answer:Calculate the area of this triangle - OCR - GCSE Maths - Question 18 - 2018 - Paper 1

Step 1

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Answer

To find the area of the triangle, we first need to use the cosine rule to find one of the angles. We denote the sides as follows:

Using the cosine rule:

$c^2 = a^2 + b^2 - 2ab \cos(C)$

Substituting the values:

$(3.9)^2 = (6.4)^2 + (5.8)^2 - 2 \cdot (6.4) \cdot (5.8) \cdot \cos(C)$

Solving this will give us the value for cos(C), and hence the angle C.

Step 2

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Answer

With the angle C determined, we can calculate the area of the triangle using the formula:

$\text{Area} = \frac{1}{2}ab \sin(C)$

Substituting the values for a, b, and the angle C we calculated:

$\text{Area} = \frac{1}{2} \cdot 6.4 \cdot 5.8 \cdot \sin(C)$

Solving this will give the area in square centimeters.

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