Mensuration formulas
Square
2
𝐴𝑟𝑒𝑎 = 𝑙
𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 = 4𝑙
𝑙 = 𝑙𝑒𝑛𝑔𝑡ℎ
Rectangle
𝐴𝑟𝑒𝑎 = 𝑙 × 𝑏
𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 = 2(𝑙 + 𝑏)
𝑙 = 𝑙𝑒𝑛𝑔𝑡ℎ , 𝑏 = 𝑏𝑟𝑒𝑎𝑑𝑡ℎ
Triangle
1
𝐴𝑟𝑒𝑎 = 2
×𝑏×ℎ
𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 = 𝑎 + 𝑏 + 𝑐
𝐻𝑒𝑟𝑜𝑛´𝑠 𝐹𝑜𝑟𝑚𝑢𝑙𝑎:
𝑎+𝑏+𝑐
𝑆= 2
𝐴 = 𝑆(𝑆 − 𝑎)(𝑆 − 𝑏)(𝑆 − 𝑐)
Equilateral Triangle
3 2
𝐴𝑟𝑒𝑎 = 4
𝑙
𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 = 3𝑎
Parallelogram
𝐴𝑟𝑒𝑎 = 𝑏 × ℎ
𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 = 2(𝑎 + 𝑏)
Rhombus
1
𝐴𝑟𝑒𝑎 = 2
× 𝑑1 × 𝑑2
𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 = 4𝑎
Trapezium(Trapeziod)
1
𝐴𝑟𝑒𝑎 = 2
(𝑎 + 𝑏) × ℎ
Kite
1
𝐴𝑟𝑒𝑎 = 2
× 𝑑1 × 𝑑2
𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 = 2(𝑎 + 𝑏)
𝑊ℎ𝑒𝑟𝑒 𝑎 𝑎𝑛𝑑 𝑏 𝑎𝑟𝑒 𝑡ℎ𝑒 𝑙𝑒𝑛𝑔𝑡ℎ𝑠 𝑜𝑓 𝑡ℎ𝑒 𝑡𝑤𝑜 𝑑𝑖𝑠𝑡𝑖𝑛𝑐𝑡 𝑝𝑎𝑖𝑟𝑠 𝑜𝑓 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑠𝑖𝑑𝑒𝑠.
Circle
2
𝐴𝑟𝑒𝑎 = π𝑟
𝐶𝑖𝑟𝑐𝑢𝑚𝑓𝑒𝑟𝑒𝑛𝑐𝑒 = 2π𝑟
𝑟 = 𝑟𝑎𝑑𝑖𝑢𝑠
1 2
𝐴𝑟𝑒𝑎 𝑜𝑓 𝑎 𝑞𝑢𝑎𝑑𝑟𝑎𝑛𝑡 = 4
×π𝑟
1 2
𝐴𝑟𝑒𝑎 𝑜𝑓 𝑎 𝑠𝑒𝑚𝑖 − 𝑐𝑖𝑟𝑐𝑙𝑒 = 2 × π𝑟
𝑆𝑒𝑐𝑡𝑜𝑟 𝑜𝑓 𝑎 𝑐𝑖𝑟𝑐𝑙𝑒
θ 2
𝐴𝑟𝑒𝑎 = 360
× π𝑟
θ
𝐴𝑟𝑐 𝐿𝑒𝑛𝑔𝑡ℎ = 360
× 2π𝑟
θ
𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 = 2𝑟 + 360
× 2π𝑟
Cube
2
𝑇𝑜𝑡𝑎𝑙 𝑠𝑢𝑟𝑓𝑎𝑐𝑒 𝐴𝑟𝑒𝑎 = 6𝑙
3
𝑉𝑜𝑙𝑢𝑚𝑒 = 𝑙
Cuboid
𝑇𝑜𝑡𝑎𝑙 𝑠𝑢𝑟𝑓𝑎𝑐𝑒 𝐴𝑟𝑒𝑎 = 2(𝑙𝑏 + 𝑏ℎ + 𝑙ℎ)
𝑉𝑜𝑙𝑢𝑚𝑒 = 𝑙 × 𝑏 × ℎ
Cylinder
Curve surface area = 2π𝑟ℎ
𝑇𝑜𝑡𝑎𝑙 𝑠𝑢𝑟𝑓𝑎𝑐𝑒 𝐴𝑟𝑒𝑎 = 𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 = 2π𝑟(ℎ + 𝑟)
2
𝑉𝑜𝑙𝑢𝑚𝑒 =π𝑟 ℎ
Cone
2 2
𝑆𝑙𝑎𝑛𝑡 ℎ𝑒𝑖𝑔ℎ𝑡: 𝑙 = 𝑟 + ℎ
𝐶𝑢𝑟𝑣𝑒 𝑠𝑢𝑟𝑓𝑎𝑐𝑒 𝑎𝑟𝑒𝑎 = π𝑟𝑙
𝑇𝑜𝑡𝑎𝑙 𝑠𝑢𝑟𝑓𝑎𝑐𝑒 𝑎𝑟𝑒𝑎 = π𝑟(𝑙 + 𝑟)
1 2
Volume = 3
π𝑟 ℎ
𝑆𝑝ℎ𝑒𝑟𝑒
2
Surface Area = 4π𝑟
4 3
𝑉𝑜𝑙𝑢𝑚𝑒 = 3
π𝑟
Hermisphere
2
Curve surface area = 2π𝑟
2
Total Surface Area = 3π𝑟
2 3
𝑉𝑜𝑙𝑢𝑚𝑒 = 3
π𝑟
Frustum of a Cone
2 2
𝑉𝑜𝑙𝑢𝑚𝑒 =
1
3 (
πℎ 𝑅 + 𝑟 + 𝑅𝑟 )
Curve Surface Area = π(𝑅 + 𝑟)𝑙
2 2
Total Surface Area = π(𝑅 + 𝑟)𝑙 + π𝑅 + π𝑟
𝑅 = 𝑙𝑎𝑟𝑔𝑒𝑟 𝑟𝑎𝑑𝑖𝑢𝑠, 𝑟 = 𝑠𝑚𝑎𝑙𝑙𝑒𝑟 𝑟𝑎𝑑𝑖𝑢𝑠, ℎ = ℎ𝑒𝑖𝑔ℎ𝑡, 𝑙 = 𝑠𝑙𝑎𝑛𝑡 ℎ𝑒𝑖𝑔ℎ𝑡
Pyramids
1
𝑉𝑜𝑙𝑢𝑚𝑒 = 3
× 𝑏𝑎𝑠𝑒 𝑎𝑟𝑒𝑎 × ℎ𝑒𝑖𝑔ℎ𝑡
Total surface area = 𝑆𝑢𝑚 𝑜𝑓 𝑎𝑟𝑒𝑎𝑠 𝑜𝑓 𝑎𝑙𝑙 𝑓𝑎𝑐𝑒𝑠
