If the area of a trapezium is 60 square units and the lengths of the two parallel sides are 10 units and 20 units, what is the height?

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Q: If the area of a trapezium is 60 square units and the lengths of the two parallel sides are 10 units and 20 units, what is the height?

Solution: Area = (1/2) × (base1 + base2) × height. Thus, 60 = (1/2) × (10 + 20) × height, giving height = 60 / 15 = 4 units.

Steps: 8

Step 1: Understand that the area of a trapezium can be calculated using the formula: Area = (1/2) × (base1 + base2) × height.
Step 2: Identify the values given in the question. The area is 60 square units, base1 is 10 units, and base2 is 20 units.
Step 3: Substitute the known values into the area formula: 60 = (1/2) × (10 + 20) × height.
Step 4: Calculate the sum of the bases: 10 + 20 = 30.
Step 5: Substitute this sum back into the equation: 60 = (1/2) × 30 × height.
Step 6: Simplify (1/2) × 30 to get 15. Now the equation is: 60 = 15 × height.
Step 7: To find the height, divide both sides of the equation by 15: height = 60 / 15.
Step 8: Calculate 60 divided by 15, which equals 4. Therefore, the height is 4 units.