Page 249 - ICSE Math 7

Step 3: Cut the parallelogram along the altitude to separate regions I and II. Paste regions I and
II in the interchanged positions to form a rectangle as shown.

A′ A″ D A″ D A′ A″ D(A′)

I II II I

B E′ E″ C E″ C B E′ E″ C(B) E′

Thus, area of parallelogram = Area of rectangle

= length × breadth Altitude
(breadth)
= base × altitude

A Base (length)
II: Area of a triangle
Step 1: Draw a triangle ABC on a white sheet of paper.

B C

A′

Step 2: Using a tracing paper, draw a ∆ A′B′C′ which
should be an exact replica of triangle ABC
and cut it out.
B′ C′

Step 3: Now paste the cut out of ∆ A′B′C′ along ∆ ABC such that C′ coincides with A,
A′ coincides with C and B′ is opposite to vertex B (see figure).

C′ B′
A A(C′) B′

Altitude (h)

A′
B C B Base (b) C(A′)
Step 4: Area of triangle is half of the area of the parallelogram so formed.
1 1 1
Thus area of triangle = (area of parallelogram) = (base × altitude) = × b × h
2 2 2

235