In trapezium ABCD with AB ∥ CD and AB < CD, suppose CD = 6 cm and the distance (height) between the parallel sides is 4 cm.\nIf 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

← Previous Question Next Question→

More Questions from Area

A circle has area 346.5 cm².\nFind its circumference (in centimetres).
Total surface area of a cube (side = 7.5 cm)\nFind the total surface area (in cm²) of a cube whose edge length is 7.5 cm.
Circle vs rectangle with perimeter 50 cm\nThe area of a circle equals the area of a rectangle whose perimeter is 50 cm and whose length exceeds its breadth by 3 cm. Find the diameter of the circle (in cm).
Square from its diagonal (14 cm)\nThe diagonal of a square is 14 cm. Compute the area of the square (in cm²).
Two externally touching circles\nTwo circles touch externally. The distance between their centres is 12 cm. If the radius of one circle is 7 cm, find the diameter (in cm) of the other circle.
Rhombus from area and one diagonal\nThe area of a rhombus is 84 cm² and one diagonal measures 7 cm. Find the length of the other diagonal (in cm).
Perimeter of a semicircle (radius = 28 cm)\nFind the perimeter of a semicircle of radius 28 cm (use perimeter = πr + 2r).
Cyclic quadrilateral angle bisectors meet the circle\nABCD is a quadrilateral inscribed in a circle of radius r. The internal bisectors of ∠DAB and ∠BCD meet the circumcircle again at X and Y, respectively. Find the length of XY.
Canvas needed for a tent (cylinder + cone, r = 10 m)\nA tent is formed by a cylinder of radius 10 m and height 5 m, surmounted by a cone of the same radius with slant height 15 m. How much canvas is required if 20% extra is allowed for folding/stitching? (Use π = 22/7. Ignore floor.)
Earthwork spread from a cylindrical ditch\nA square field has area X m². A cylindrical ditch of radius 7 m and depth 2 m is dug; the removed earth is spread uniformly over the remaining part of the field (excluding the circular ditch), raising its level by 0.77 m. Find X.

Discussion & Comments

No comments yet. Be the first to comment!

Join Discussion

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.\nIf area(ABCD) = 16 cm², find the length AB.

More Questions from Area

Discussion & Comments

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