SATHEE: Geometry Formulas

Geometry Formulas

Figure	Area (A)	Perimeter (P) / Circumference (C)	Mnemonic
Square (a)	a²	4a	“A-Square, P-Four-a”
Rectangle (l,b)	l × b	2(l+b)	“L-Bee, Two-L-B”
Triangle (b,h)	½ b h	a+b+c	“Half-base-height”
Equilateral Δ	(√3/4) a²	3a	“Root-3-four-a-square”
Right Δ	½ × product of legs	a+b+hypotenuse	“Legs-half”
Circle (r)	π r²	2πr	“Pi-r-sq, Two-pi-r”
Semi-circle	½ π r²	πr + 2r	“Half-pi-r-sq, pi-r-plus-dia”

Solid	Volume (V)	Total Surface Area (TSA)	Lateral/Curved SA	Trick
Cuboid (l,b,h)	l b h	2(lb+bh+hl)	2h(l+b)	“L-B-H, wrap gift twice”
Cube (a)	a³	6a²	4a²	“Six faces, four sides”
Cylinder (r,h)	π r² h	2πr(r+h)	2πrh	“Pie-r-sq-h, two-pi-r-(r+h)”
Cone (r,h,l)	⅓ π r² h	π r(r+l)	π r l	“One-third pie, slant-l”
Sphere (r)	4/3 π r³	4π r²	—	“Four-thirds pie-r-cube”
Hemisphere	2/3 π r³	3π r²	2π r²	“Half-sphere, 3-pi-r-sq”

Slant height l = √(r²+h²)

Diagonal of a square of side 8 cm is
a) 8 cm b) 8√2 cm c) 16 cm d) 4√2 cm
Area of equilateral triangle with side 4 cm (approx)
a) 6.9 cm² b) 8.3 cm² c) 5.2 cm² d) 7.1 cm²
Volume of sphere of radius 3 cm (π=3.14)
a) 84.78 cm³ b) 113.04 cm³ c) 28.26 cm³ d) 37.68 cm³
Curved surface area of cylinder (r=7 cm, h=10 cm)
a) 440 cm² b) 308 cm² c) 154 cm² d) 880 cm²
Perimeter of semi-circle of diameter 14 cm (π=22/7)
a) 22 cm b) 36 cm c) 44 cm d) 50 cm
Diagonal of cube of side 5 cm is
a) 5√3 cm b) 5√2 cm c) 10 cm d) 15 cm
Area of trapezium with parallel sides 10 cm, 6 cm & height 4 cm
a) 32 cm² b) 64 cm² c) 16 cm² d) 28 cm²
If circumference is 44 cm, radius is
a) 7 cm b) 14 cm c) 3.5 cm d) 21 cm
Slant height of cone (r=6 cm, h=8 cm)
a) 10 cm b) 14 cm c) 9 cm d) 12 cm
Ratio of volumes of two spheres of radii 2 cm & 3 cm is
a) 8 : 27 b) 4 : 9 c) 2 : 3 d) 1 : 3

Answers

1-b 2-a 3-b 4-a 5-b 6-a 7-a 8-a 9-a 10-a