NCERT Solutions Ganita Prakash Chapter 6 Areas of triangles on grid paper — In-text Questions
Book page 143 & 144 Updated on2026-09-05
Q1.
Find the area of blue triangle BAD. __________
Answer
First read the grid. Rectangle ABCD is 5 units long and 4 units wide, and the blue triangle BAD is one half of it, cut by the diagonal DB.
Rectangle ABCD on grid paper. The blue triangle BAD is half the rectangle; the red triangle ABE stands on the same base AB with the same height.
Area of rectangle ABCD = 5 × 4 = 20 sq units
Area of triangle BAD = ½ × 20 = 10 sq units
Answer: 10 square units.
Check by counting: the triangle covers 10 full squares plus 4 halves and leaves 8 halves out — 10 squares in all. ✔
Q2.
Find the area of red triangle ABE. ___________
Answer
Drop the line EF straight down from E to the base AB. It cuts the red triangle into two right triangles, and the rectangle into two smaller rectangles.
AF = 3 units, FB = 2 units, height = 4 units
Area of triangle AEF = ½ of rectangle AFED = ½ × (3 × 4) = 6 sq units
Area of triangle BEF = ½ of rectangle BFEC = ½ × (2 × 4) = 4 sq units
Area of triangle ABE = 6 + 4 = 10 sq units
Answer: 10 square units — exactly the same as the blue triangle, although the two triangles look completely different.
Why they are equal: both triangles stand on the same base AB (5 units) and both have the same height (4 units, the distance between the two horizontal lines). Any triangle on this base with its top vertex anywhere on the line DC has area ½ × 5 × 4 = 10 sq units.
Q3.
Area of rectangle ABCD = ________________
Answer
Area of rectangle ABCD = length × width
= AB × AD
= 5 units × 4 units = 20 square units
And so, as the book states, the area of triangle BAD is half of this — 10 square units.
The area of a triangle is half the area of a rectangle with the same base and the same height.
Area of a triangle = ½ × base × height
Two extra points that come out of this page:
A triangle does not have to be right-angled for the rule to work. Any triangle can be split by its height into two right triangles, each of which is half of a rectangle (as with triangle ABE = ½ AFED + ½ BFEC = ½ ABCD).
Triangles that look very different can have the same area, as long as their base and height are the same.