If the area of a trapezium is 60 cm² and the lengths of the two parallel sides a

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Question: If the area of a trapezium is 60 cm² and the lengths of the two parallel sides are 10 cm and 14 cm, what is the height?

Options:

Correct Answer: 5 cm

Solution:

Area = (1/2) × (a + b) × height. 60 = (1/2) × (10 + 14) × height. Solving gives height = 5 cm.

If the area of a trapezium is 60 cm² and the lengths of the two parallel sides are 10 cm and 14 cm, what is the height?

If the area of a trapezium is 60 cm² and the lengths of the two parallel sides are 10 cm and 14 cm, what is the height?

Step 1: Write down the formula for the area of a trapezium: Area = (1/2) × (a + b) × height.
Step 2: Identify the values given in the question: Area = 60 cm², a = 10 cm, b = 14 cm.
Step 3: Substitute the values into the formula: 60 = (1/2) × (10 + 14) × height.
Step 4: Calculate (10 + 14) to get 24: 60 = (1/2) × 24 × height.
Step 5: Simplify (1/2) × 24 to get 12: 60 = 12 × height.
Step 6: To find height, divide both sides by 12: height = 60 / 12.
Step 7: Calculate 60 / 12 to get 5: height = 5 cm.

Area of a Trapezium – The formula for the area of a trapezium is A = (1/2) × (a + b) × height, where a and b are the lengths of the parallel sides.
Solving for Height – Rearranging the area formula to solve for height requires basic algebraic manipulation.