NCERT Solutions Ganita Prakash (Part 2) Chapter 7 Finding the Area Using Two Copies of the Trapezium — In-text Questions

Book page 168 Updated on2026-09-05

Q1.

What figure will we get when the two trapeziums are joined along BC? The possibilities are either a 6-sided figure or a 4-sided figure (quadrilateral).

Answer

We get a quadrilateral. The 6-sided possibility is ruled out by an angle count.

AB ‖ CD, and BC is a transversal, so the interior angles on the same side add to 180°:
x + y = 180°

At B, the angles x and y of the two copies sit next to each other and make a straight angle,
so A, B and D′ lie on one straight line.
In the same way, A′, C and D lie on one straight line.

With those two pairs of edges straightening out, the joined figure has only four corners — it is a quadrilateral.

Why it happens: the second copy is the first one turned through a half-turn, so the angle that arrives at B is the trapezium's other angle on that side. Parallel sides force those two angles to be supplementary, which is exactly the condition for the two edges to line up into one straight edge instead of forming a corner.

Q2.

What type of a quadrilateral is this?

Answer

A parallelogram.

The other pair of angles of the trapezium also satisfies u + v = 180°
These are the interior angles on the same side of the transversal A′D
so AD ‖ D′A′

We already have AD′ ‖ A′D from the first pair of straight lines.
Both pairs of opposite sides are parallel → AD′A′D is a parallelogram

Its base is a + b and its height is h, and it is made of exactly two copies of the trapezium.

Area of the trapezium = ½ × Area of the parallelogram
= ½ × (a + b) × h
= ½ h(a + b)

Why it happens: this is the shortest of all the derivations. Nothing is cut — a second copy is simply turned round and set alongside. Because the two copies are congruent, the parallelogram has exactly twice the area, and a parallelogram's area we already know.

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