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NCERT Solutions Ganita Prakash (Part 2) Chapter 7 Area of any Polygon — In-text Questions

Book page 159 Updated on2026-09-05

Q1.
How do we find the area of this quadrilateral? What measurements do we need for this?
Answer

Split it into two triangles with a diagonal, and add their areas.

For quadrilateral ABCD, join BD. Now ABCD = ∆ABD + ∆CBD, and both triangles stand on the same base BD.

Measure: the diagonal BD, and the two heights — the perpendicular from A to BD and the perpendicular from C to BD.

Area (ABCD) = ½ × BD × h₁ + ½ × BD × h₂
= ½ × BD × (h₁ + h₂)
Why it happens: a diagonal separates the quadrilateral into two pieces that do not overlap and together make the whole, so the areas simply add. Because both triangles share the diagonal as base, the two heights can be added first, which saves work.
Q2.
How do we find the area of this pentagon?
Answer

The same way — cut it into triangles.

Pick one vertex of the pentagon and join it to the two non-neighbouring vertices. That gives three triangles. Measure each triangle's base and height, and add the three areas.

A pentagon (5 sides) → 3 triangles
In general, an n-sided polygon → n − 2 triangles
Tip: for an awkward polygon it is often easier to enclose it in a rectangle and subtract the corner triangles, rather than to add up many small pieces.
Q3.
Can any polygon be divided into triangles?
Answer

Yes. Every polygon can be cut into triangles by drawing diagonals inside it.

Why it happens: a polygon has straight sides, and any region bounded by straight lines can be sliced up by more straight lines until only three-sided pieces are left. For a convex polygon this is easy — join one vertex to all the others. For a polygon that caves inwards you may have to choose the diagonals more carefully, but a set that works always exists.

This is why the triangle formula is the key to the whole chapter:

Know ½ × base × height  →  know the area of any polygon
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