NCERT Solutions for Class 5th Maths Chapter 11 Making new shapes with the same area; comparing a square with a triangle — Let Us Do
Book page 149–150 Updated on2026-09-19
Q1.
Draw different shapes having the same area as the given shape. Write the perimeter of each shape. What do you notice? Discuss.
The given shape on a 1 cm square grid. The empty part of the grid is for the shapes you draw.
Answer
The given shape is 9 squares across and 2 squares down, so its area is 18 square cm and its perimeter is 22 cm. Every new shape you draw must also cover 18 squares.
Find the area of the given shape. 9 × 2 = 18 square cm.
Find pairs of numbers that multiply to 18. 1 × 18, 2 × 9, 3 × 6. Each pair gives a rectangle of area 18.
Draw those rectangles on your grid: 18 × 1, 9 × 2 and 6 × 3.
Draw a shape that is not a rectangle too — for example a wide block of 3 rows of 4 with a smaller block of 3 rows of 2 stuck under it. Count: 12 + 6 = 18 squares.
Write the perimeter beside each shape. Walk round the outline and count the 1 cm sides.
Shape (all 18 square cm)
Perimeter
18 × 1 rectangle
2 × (18 + 1) = 38 cm
9 × 2 rectangle (the given one)
2 × (9 + 2) = 22 cm
6 × 3 rectangle
2 × (6 + 3) = 18 cm
L-shape (4 wide top, 2 wide foot)
22 cm
What we notice: All these shapes need exactly the same amount of cloth — 18 square cm. But the lace they need is completely different, from 18 cm up to 38 cm. The fatter the shape, the less lace. The 6 × 3 rectangle is the closest to a square, and it has the smallest perimeter of the four.
Sample answer for the discussion: “We drew four shapes, all with an area of 18 square cm. Their perimeters were 38 cm, 22 cm, 18 cm and 22 cm. So shapes with the same area can have different perimeters, and the shape nearest to a square has the smallest perimeter.”
Q2.
Is the area of shape (a) less than the area of shape (b) given below? Discuss.
Shape (a) is a square on the grid. Shape (b) is a triangle on the same grid.
Answer
No. The two areas are equal — each shape covers 9 square cm.
Both cover 9 square cm, even though one is a square and the other a triangle.
Shape (a). It is a square, 3 grid squares across and 3 down. Area = 3 × 3 = 9 square cm.
Shape (b). Its flat top edge is 6 squares long and it comes down to a point 3 squares below.
Think of the rectangle it fits inside. A 6-by-3 rectangle holds 6 × 3 = 18 squares.
Take half. The triangle is exactly half of that rectangle. Area = 18 ÷ 2 = 9 square cm.
Compare. 9 = 9, so neither shape is less than the other.
Area of (a) = 3 × 3 = 9 square cm Area of (b) = (6 × 3) ÷ 2 = 18 ÷ 2 = 9 square cm The areas are equal
Why the triangle is half the rectangle: Draw the 6 × 3 rectangle round the triangle. The two empty corners left over can be slid together and they fill exactly one more triangle the same size as the first. So the rectangle is made of two of these triangles, and the triangle is half of it.
Check it yourself by counting: On the grid the triangle covers 6 whole squares plus 6 half squares. 6 + (6 × ½) = 6 + 3 = 9 square cm. The same answer.