NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 6: Mensuration - Problems and SolutionsQuestion 59
Class 6 - Mathematics - Unit 6: Mensuration - Problems and Solutions
Question. 59
Find area and perimeter of figures in Fig. 6.20 if each square = 1 sq cm.
Answer:
(i) 12 cm², 14 cm
(ii) 12 cm², 16 cm
(iii) 12 cm², 14 cm
Detailed Answer with Explanation:
- Area = number of small squares covered by the figure.
- Perimeter = total length of the outer boundary of the figure.
- Count each full square as (1) sq cm.
- Two half squares make (1) full square.
- For perimeter, walk along the outside edges only. Do not count inner edges.
- Each edge of one small square is (1) cm.
(i) Figure (i)
- Area
- Count the filled squares: suppose you find (12) squares in total.
- Write it step by step:
- ( ext{Area} = 12 imes 1 ext{ cm}^2)
- ( ext{Area} = 12 ext{ cm}^2)
- Perimeter
- Trace the outer border and count each small edge you walk.
- Suppose the total outer edges are (14).
- ( ext{Perimeter} = 14 imes 1 ext{ cm})
- ( ext{Perimeter} = 14 ext{ cm})
- Answer (i): (12 ext{ cm}^2), (14 ext{ cm})
(ii) Figure (ii)
- Area
- Count all filled/covered squares. You get (12).
- ( ext{Area} = 12 imes 1 ext{ cm}^2)
- ( ext{Area} = 12 ext{ cm}^2)
- Perimeter
- Go around the outside only and count the small edges.
- Total outer edges here are (16).
- ( ext{Perimeter} = 16 imes 1 ext{ cm})
- ( ext{Perimeter} = 16 ext{ cm})
- Answer (ii): (12 ext{ cm}^2), (16 ext{ cm})
(iii) Figure (iii)
- Area
- Count the filled squares again: (12).
- ( ext{Area} = 12 imes 1 ext{ cm}^2)
- ( ext{Area} = 12 ext{ cm}^2)
- Perimeter
- Trace the outer boundary and count each unit edge.
- Total outer edges are (14).
- ( ext{Perimeter} = 14 imes 1 ext{ cm})
- ( ext{Perimeter} = 14 ext{ cm})
- Answer (iii): (12 ext{ cm}^2), (14 ext{ cm})
Quick self-check
- If two shapes cover the same number of small squares, their area is the same.
- Different outlines can give different perimeters even when areas match.