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NCERT Solutions Ganita Prakash Chapter 6 In-text Questions — Area of a Triangle

Book page 142 Updated on2026-09-05

Q1.
Check! whether the two triangles overlap each other exactly. Do they have the same area?
Answer

Yes — they overlap exactly, and so they have the same area.

Draw a rectangle, cut along one diagonal and place one triangle on top of the other (turn it round if needed). Every corner matches and no part sticks out.

The two triangles are exactly the same size and shape.
So each one is half of the rectangle.

Try it with a long thin rectangle, a nearly square one, and a square. The result is always the same. For a square, cutting along a diagonal gives two equal right-angled triangles.

Why the diagonal halves the rectangle: the diagonal splits the rectangle into two triangles with the same base, the same height and the same right angles. Rotate one by half a turn and it sits perfectly on the other.
Q2.
Can you draw any inferences from this exercise? Please write it here.
Answer

Two clear inferences:

  1. A diagonal divides a rectangle (or a square) into two triangles of equal area.
  2. Therefore the area of each such triangle = half the area of the rectangle, that is
    Area of the triangle = ½ × length × width

A third, more general inference follows from this: two figures can look completely different yet have exactly the same area, because area is about how much region is covered, not about shape.

Q3.
Now, see the figures below. Is the area of the blue rectangle more or less than the area of the yellow triangle? Or is it the same? Why?
Answer

The two areas are the same.

Look carefully at the measurements in the figure. The yellow triangle stands on a base that is twice as long as the blue rectangle, and both figures have the same height.

Let the rectangle be l long and h high → area = l × h
The triangle has base 2l and height h → area = ½ × 2l × h = l × h
So the two areas are equal.
Why: the dotted height line splits the yellow triangle into two right triangles. Each of them is half of a small rectangle, and the two small rectangles together are the same size as the blue rectangle counted twice. Halving and doubling cancel out — the areas match.
Q4.
Can you see some relationship between the blue rectangle and the yellow triangle and their areas? Write the relationship here.
Answer

The relationship is:

Area of a triangle = ½ × base × height

In words: a triangle covers half of the rectangle that has the same base and the same height. Here the triangle's base is double, so its area comes out equal to the blue rectangle:

Triangle = ½ × (2 × rectangle's length) × height = rectangle's area
Check it on grid paper: draw a rectangle 6 units × 4 units (area 24). Now draw a triangle with base 6 units and height 4 units — count its squares and you will get 12, exactly half. ✔
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