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Mensuration 2D / 3D

Lesson 54 of 113

1. Ye topic hai kya?

Mensuration = kitna lamba (perimeter) aur kitna phaila (area / volume). Boats P10 yahi: rectangle 8 m × 6 m, area 48 m² — 48 km trip nahi.

Paper yahan kya maangta

l×b, 2(l+b), square, path around, ½bh, Heron, rhombus ½ d₁d₂, trapezium ½(a+b)h, circle 2πr / πr² (poora), cuboid V=lbh, sirf 4 deewar 2(l+b)h, tiles ginti.

Yahan kya nahi

Sector θ/360, segment, ring leftover — Areas related. CSA/TSA, frustum, painted n³ — Surface areas. 16×12 tile HCF 4 — HCF/LCM. Still 12 current 4 — Boats. Bar-graph — DI.

Rectangle: A = l × b, P = 2(l + b). Path = outer − inner.
Cuboid: V = l b h. 4 walls (ceiling/floor nahi): 2(l + b)h.

2. 8 × 6 = 48, path alag

Area 48, perimeter 2(14)=28 m. Fence 28 pe chalti, carpet 48 pe. Square side 9: A=81, P=36.

48 m² 8 m 6 m P = 28 m · boat 48 km nahi

Andar = area. Bahar ki line = perimeter.

1 m path around: outer 10 × 8 = 80, path = 80 − 48 = 32 m². Yeh ring π(R²−r²) nahi — wahan circle chapter.

48 path 32

Bahar patti = path 32. HCF 16×12 tiles nahi.

Example

8 m × 6 m. Area aur perimeter? (Boats P10.)

Solution

  1. l×b, 2(l+b)

    48 m², 28 m. 48 km down-up nahi.

Answer48 m², 28 m
Example

Usi around 1 m path. Path area?

Solution

  1. 80−48

    32. 2×28×1=56 (sirf agar corners double-count na ho — rectangle path corners included in outer−inner).

Answer32 m²

3. Triangle, rhombus, trapezium, circle

½ × 10 × 8 = 40 (8×6 ka aadha 24 mat — alag triangle). Right 9-12-15: ½×9×12=54.

Heron 13, 14, 15: s=21, √[21×8×7×6]=√7056=84.

Parallelogram 11 × h 6 = 66. Rhombus diagonals 10, 24: ½×10×24=120. Trapezium 10+16, h=7: ½×26×7=91.

Circle r=10, π=3.14: C=62.8, A=314. (r=14 → 88/616 Areas-related pe; sector/ring wahan.)

Example

Sides 13, 14, 15. Area?

Solution

  1. s=21

    √7056=84. ½×13×14 mat (base-height nahi diye).

Answer84

4. Cuboid, 4 walls, tiles

Room 8 × 6 × 5: volume 240 m³. Floor carpet = 48 m² (wahi rectangle). Sirf 4 deewar = 2(8+6)×5 = 140 m² — ceiling+floor Surface-areas whitewash 2h(l+b)+lb alag.

Cube side 5: V=125, TSA=150. Painted n³ cubes nahi.

Tiles 40 cm × 40 cm on 8 m × 6 m: 0.4 m, 20 × 15 = 300 tiles. (16×12 room, tile 4, count 12 — HCF/LCM.)

Area ko perimeter mat. Path pe sirf 2(l+b)×width corners chhoot/double. Sector leftover Areas-related. Frustum / CSA Surface areas. Boat 16+8 still. Graph DI.
Example

8×6×5 room. 4 walls?

Solution

  1. 2(14)×5

    140 m². TSA 2(lb+bh+hl)=2(48+30+40)=236 alag.

Answer140 m²
Example

8×6 floor, 40 cm tiles. Kitni?

Solution

  1. 20×15

    300. HCF 12 nahi.

Answer300

5. Sawal — basic se pro

Q1 · Basic

8 m × 6 m. Area?

  1. 48 m²
  2. 28 m²
  3. 14
  4. 48 km

Solution

  1. 48

    B perimeter number. D boat.

Answer48 m²
Q2 · Basic

Uska perimeter?

  1. 28 m
  2. 48 m
  3. 14 m
  4. 36 m

Solution

  1. 2×14

    28.

Answer28 m
Q3 · Basic

1 m path around. Path area?

  1. 32 m²
  2. 28 m²
  3. 80
  4. 16

Solution

  1. 80−48

    32. C outer whole.

Answer32 m²
Q4 · Medium

½ × 10 × 8 triangle. Area?

  1. 40
  2. 24
  3. 80
  4. 18

Solution

  1. 40

    B ½×8×6 rectangle mix.

Answer40
Q5 · Medium

13, 14, 15. Heron area?

  1. 84
  2. 91
  3. 105
  4. 42

Solution

  1. √7056

    84.

Answer84
Q6 · Medium

Rhombus d=10, 24. Area?

  1. 120
  2. 240
  3. 34
  4. 60

Solution

  1. ½×10×24

    120. B bina ½.

Answer120
Q7 · Medium

Trapezium 10+16, h=7. Area?

  1. 91
  2. 112
  3. 70
  4. 26

Solution

  1. ½×26×7

    91.

Answer91
Q8 · Pro

8×6×5. 4 walls?

  1. 140 m²
  2. 240
  3. 236
  4. 48

Solution

  1. 2×14×5

    140. B volume. C TSA. D floor.

Answer140 m²
Q9 · Pro

8×6 floor, 40 cm tiles. Count?

  1. 300
  2. 12
  3. 48
  4. 192

Solution

  1. 20×15

    300. B HCF 16-12-4.

Answer300
Q10 · Pro

Still 12, current 4, down 16. Is chapter?

  1. Nahi — Boats
  2. Haan, 16 m side
  3. Path 16
  4. Volume 16

Solution

  1. Nadi

    A.

AnswerA

Practice

Pehle khud, phir neeche kholo.

12345 678910

P1

Square side 9. Area?

  1. 81
  2. 36
  3. 18
  4. 72

Solution

  1. 81

    B perimeter.

Answer81
P2

9-12-15 right triangle. Area?

  1. 54
  2. 108
  3. 36
  4. 67.5

Solution

  1. ½×9×12

    54.

Answer54
P3

Parallelogram 11, h=6. Area?

  1. 66
  2. 34
  3. 33
  4. 84

Solution

  1. 11×6

    66. D Heron mix.

Answer66
P4

Circle r=10, π=3.14. Area?

  1. 314
  2. 62.8
  3. 616
  4. 31.4

Solution

  1. πr²

    314. B C. C r=14 Areas-related.

Answer314
P5

Cuboid 8×6×5. Volume?

  1. 240
  2. 140
  3. 48
  4. 19

Solution

  1. 240

    .

Answer240
P6

Cube side 5. TSA?

  1. 150
  2. 125
  3. 30
  4. 25

Solution

  1. 6a²

    150. B volume. Painted n³ nahi.

Answer150
P7

Carpet ₹50/m² on 8×6. Cost?

  1. 2400
  2. 1400
  3. 2800
  4. 50

Solution

  1. 48×50

    2400. B walls 140.

Answer2400
P8

r=14, 90° sector leftover. Is chapter?

  1. Nahi — Areas related
  2. Haan, 56 path
  3. Mensuration sector
  4. Ring 32

Solution

  1. θ/360

    A.

AnswerA
P9

Frustum l, CSA π(R+r)l. Is chapter?

  1. Nahi — Surface areas
  2. Haan, trapezium
  3. Path frustum
  4. Cone 2D

Solution

  1. 3D bucket

    A.

AnswerA
P10

Bar graph se kitna % padho. Is chapter?

  1. Nahi — Data interpretation
  2. Haan, area of bars
  3. 48 as height
  4. Tiles graph

Solution

  1. Chart

    A. Agle pe.

AnswerA

← Index · Boats · Areas related

Agle topic: Data interpretation.