NCERT Solutions for Class 6th Maths Chapter 6 Finding a missing length or a missing area — Area Maze Puzzles
Book page 148 Updated on2026-09-19
Q1.
In each figure, find the missing value of either the length of a side or the area of a region. — Puzzle a.
Puzzle a — a rectangle cut by one vertical and one horizontal line into four smaller rectangles (page 148).
Answer
The big rectangle is cut by one vertical line and one horizontal line, so the four small rectangles share their sides in pairs.
Top row: 13 and 26 sit on the same height
26 ÷ 13 = 2, so the right column is twice as wide as the left column
Bottom row: both rectangles sit on the same height too
? = 2 × 15 = 30 sq cm
Answer: 30 sq cm.
Why no lengths are needed: for rectangles of the same height, area is proportional to width. Doubling the width doubles the area, whatever the actual measurements are.
Q2.
In each figure, find the missing value of either the length of a side or the area of a region. — Puzzle b.
Puzzle b — three rectangles forming a step, with the lengths printed in the book (page 148).
Answer
Work up from the bottom rectangle.
Bottom rectangle: area 10, height 2 → width = 10 ÷ 2 = 5 cm
Its left part is 3 cm, so the upright rectangle is 5 − 3 = 2 cm wide
Upright rectangle: area 10, width 2 → height = 10 ÷ 2 = 5 cm
The shaded rectangle starts 2 cm above the bottom rectangle,
so its height = 5 − 2 = 3 cm, and its width is 3 cm
? = 3 × 3 = 9 sq cm
Answer: 9 sq cm.
Q3.
In each figure, find the missing value of either the length of a side or the area of a region. — Puzzle c.
Puzzle c — three rectangles forming a staircase, with the lengths printed in the book (page 148).
Answer
Start with the middle rectangle, because both its area and its height are known.
Middle rectangle: area 42, height 6 → width = 42 ÷ 6 = 7 cm
Bottom rectangle: width = 7 + 5 = 12 cm
Its area is 60, so its height = 60 ÷ 12 = 5 cm
Total height is 15 cm, so the top rectangle's height = 15 − 6 − 5 = 4 cm
Its width = 7 − 3 = 4 cm
? = 4 × 4 = 16 sq cm
Answer: 16 sq cm.
Strategy for area mazes: always begin at the rectangle where you know two facts (an area and a length). Each answer unlocks the next one, like a chain.
Q4.
In each figure, find the missing value of either the length of a side or the area of a region. — Puzzle d.
Puzzle d — two rectangles standing on the same base line (page 148).
Answer
The two rectangles stand side by side on the same base line.
Right rectangle: area 18, width 5 → height = 18 ÷ 5 = 3.6 cm
The left rectangle rises 4 cm higher, so its height = 3.6 + 4 = 7.6 cm
Left rectangle: area 38, height 7.6 → width = 38 ÷ 7.6 = 5 cm
Answer: the missing length is 5 cm.
Check it yourself: 5 × 7.6 = 38 ✔ and 5 × 3.6 = 18 ✔