2D Mensuration – Area & Perimeter
| Shape | Area Formula | Perimeter Formula | Example (units in cm) |
|---|---|---|---|
| Square | A=a2 | P=4a | a=5⇒ A=25,P=20 |
| Rectangle | A=l×b | P=2(l+b) | l=6, b=4 ⇒ A=24, P=20 |
| Circle | A=πr2 | C=2πr | r=3 ⇒ A≈28.27, C≈18.85 |
| Triangle | A=1/2×b×h | P=a+b+c | b=6, h=4 ⇒ A=12 |
| Equilateral Triangle | A=3/4×a2 | P=3a | a=6 ⇒ A≈15.59, P=18 |
| Parallelogram | A=b×h | P=2(a+b) | b=5, h=3 ⇒ A=15 |
| Rhombus | A=1/2×d1×d2 (diagonal) | P=4a | d1=6, d2=4 ⇒ A=12 |
| Trapezium | A=1/2×h×(a+b) | P=a+b+c+d | a=6, b=4, h=5 ⇒ A=25 |
📦 3D Mensuration – Volume & Surface Area
| Solid | Volume Formula | Surface Area Formula | Example (units in cm) |
|---|---|---|---|
| Cube | V=a3 | SA=6a2 | a=3 ⇒ V=27, SA=54 |
| Cuboid | V=l×b×h | SA=2(lb+bh+hl) | l=4, b=3, h=2 ⇒ V=24, SA=52 |
| Cylinder | V=πr2h | SA=2πr(h+r) | r=3, h=5 ⇒ V≈141.37, SA≈150.8 |
| Cone | V=1/3πr2h | SA=πr(r+l) | r=3, h=4, l=5 ⇒ V≈37.7, SA≈75.4 |
| Sphere | V=4/3πr3 | SA=4πr2 | r=3 ⇒ V≈113.1, SA≈113.1 |
| Hemisphere | V=2/3πr3 | SA=3πr2 | r=3 ⇒ V≈56.55, SA≈84.8 |
| Frustum of Cone | V=1/3πh(R2+r2+Rr) | SA=π(R+r)l+π(R2+r2) | R=5, r=3, h=4, l=5 ⇒ V≈251.3 |
π = 22/7
SA = Surface Area
V = Volume
R = Radius