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Introduction / Context:Trapezium (trapezoid) area is half the sum of parallel sides times the height. With area and one base given, solve for the other base. Given Data / Assumptions: CD = 6 cm (larger base), AB is smaller base. Height h = 4 cm; Area = 16 cm². Concept / Approach:Area formula: A = (1/2) * (AB + CD) * h. Step-by-Step Solution: 16 = (1/2) * (AB + 6) * 416 = 2 * (AB + 6) ⇒ AB + 6 = 8 ⇒ AB = 2 cm Verification / Alternative check:Plug back: A = (1/2)*(2+6)*4 = (1/2)*8*4 = 16 cm², correct. Final Answer:2 cm

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In trapezium ABCD with AB ∥ CD and AB < CD, suppose CD = 6 cm and the distance (height) between the parallel sides is 4 cm. If area(ABCD) = 16 cm², find the length AB.

Difficulty: Easy

1 cm
3 cm
2 cm
8 cm

Correct Answer: 2 cm

Explanation:

Introduction / Context:Trapezium (trapezoid) area is half the sum of parallel sides times the height. With area and one base given, solve for the other base.

Given Data / Assumptions:

CD = 6 cm (larger base), AB is smaller base.
Height h = 4 cm; Area = 16 cm².

Concept / Approach:Area formula: A = (1/2) * (AB + CD) * h.

Step-by-Step Solution:

16 = (1/2) * (AB + 6) * 416 = 2 * (AB + 6) ⇒ AB + 6 = 8 ⇒ AB = 2 cm

Verification / Alternative check:Plug back: A = (1/2)*(2+6)*4 = (1/2)*8*4 = 16 cm², correct.

Final Answer:2 cm

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In trapezium ABCD with AB ∥ CD and AB &lt; CD, suppose CD = 6 cm and the distance (height) between the parallel sides is 4 cm. If area(ABCD) = 16 cm², find the length AB.

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In trapezium ABCD with AB ∥ CD and AB < CD, suppose CD = 6 cm and the distance (height) between the parallel sides is 4 cm. If area(ABCD) = 16 cm², find the length AB.