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Here is trapezium ABCD - Edexcel - GCSE Maths - Question 19 - 2021 - Paper 1

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Question 19

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Here is trapezium ABCD. The area of the trapezium is 66cm² the length of AB: the length of CD = 2:3 Find the length of AB.

Worked Solution & Example Answer:Here is trapezium ABCD - Edexcel - GCSE Maths - Question 19 - 2021 - Paper 1

Step 1

Find dimensions based on ratio

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Answer

Let the length of CD be 3x and the length of AB be 2x, where x is a common multiplier for the lengths.

Step 2

Use area formula for trapezium

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Answer

The area of a trapezium is given by the formula:

ext{Area} = rac{1}{2} imes (AB + CD) imes ext{height}

Substituting values, we have:

66 = rac{1}{2} imes (2x + 3x) imes h

Step 3

Find height using trigonometry

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Answer

From triangle BCD, we can find the height (h) using the angle given:

sin(30^ ext{o}) = rac{h}{6}

So, h = 6 × sin(30°) = 6 × 0.5 = 3 cm.

Step 4

Substitute height into area equation

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Answer

Substituting the height back into the area formula gives:

66 = rac{1}{2} imes (5x) imes 3

This simplifies to:

66 = rac{15x}{2}

Step 5

Solve for x

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Answer

Multiplying both sides by 2:

132=15x132 = 15x

Thus:

x = rac{132}{15} = 8.8$$

Step 6

Find length of AB

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Answer

As AB = 2x, we substitute:

AB = 2 imes 8.8 = 17.6 ext{ cm}$$.

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