NCERT Solutions Ganita Prakash Chapter 6 Finding a missing length or a missing area — Area Maze Puzzles
Book page 148 Updated on2026-09-05
Q1.
In each figure, find the missing value of either the length of a side or the area of a region. — Puzzle a. (Four rectangles of areas 13 sq cm, 26 sq cm, 15 sq cm and ? sq cm.)
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. (Three rectangles: 10 sq cm with height 2 cm, 10 sq cm, and ? sq cm of width 3 cm.)
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. (A staircase of three rectangles: ? sq cm, 42 sq cm and 60 sq cm, with total height 15 cm.)
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. (Two rectangles of areas 38 sq cm and 18 sq cm; find the missing length ? cm.)
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 ✔