Non angular shape measurements

What is the sum of interior angles of a polygon with n sides?

(n−2) × 180°

What is the size of each interior angle of a regular polygon with n sides?

[(n−2) × 180°] ÷ n

What is the circumference of a circle with radius r?

C = 2πr

What is the circumference of a circle with diameter d?

C = πd

What is the area of a circle with radius r?

A = πr²

What is the surface area of a sphere with radius r?

SA = 4πr²

What is the volume of a sphere with radius r?

V = (4/3)πr³

What is the curved surface area of a hemisphere with radius r?

Curved SA = 2πr²

What is the total surface area of a hemisphere with radius r?

Total SA = 3πr²

What is the volume of a hemisphere with radius r?

V = (2/3)πr³

What is the volume of a cylinder with radius r and height h?

V = πr²h

What is the curved surface area of a cylinder with radius r and height h?

Curved SA = 2πrh

What is the total surface area of a cylinder with radius r and height h?

Total SA = 2πr² + 2πrh

What is the volume of a cone with radius r and height h?

V = (1/3)πr²h

What is the curved surface area of a cone with radius r and slant height l?

Curved SA = πrl

What is the total surface area of a cone with radius r and slant height l?

Total SA = πr² + πrl

What is the slant height of a cone with radius r and perpendicular height h?

l = √(r² + h²)

What is the volume of a triangular prism with base b, triangle height h, and length l?

V = (1/2)bhl

What is the volume of a square prism with side s and height h?

V = s²h

What is the total surface area of a square prism with side s and height h?

SA = 2s² + 4sh

What is the volume of a rectangular prism with length l, width w, and height h?

V = lwh

What is the total surface area of a rectangular prism with length l, width w, and height h?

SA = 2(lw + lh + wh)

What is the volume of a square-based pyramid with base side s and height h?

V = (1/3)s²h

What is the total surface area of a square-based pyramid with base side s and slant height l?

SA = s² + 2sl

What is the area of a triangle with base b and perpendicular height h?

A = (1/2)bh

What is the area of a triangle with two sides a and b and included angle C?

A = (1/2)ab sinC

What is the area of a kite with diagonals d₁ and d₂?

A = (1/2)d₁d₂

What is the area of a rhombus with diagonals d₁ and d₂?

A = (1/2)d₁d₂

What is the area of a rhombus with base b and perpendicular height h?

A = bh

What is the perimeter of a rhombus with side length s?

P = 4s

What is the area of a parallelogram with base b and perpendicular height h?

A = bh

What is the perimeter of a parallelogram with sides a and b?

P = 2(a + b)

What is the area of a rectangle with length l and width w?

A = lw

What is the perimeter of a rectangle with length l and width w?

P = 2(l + w)

What is the diagonal of a rectangle with length l and width w?

d = √(l² + w²)

What is the area of a trapezium with parallel sides a and b and perpendicular height h?

A = (1/2)(a + b)h

What is the area of a square with side s?

A = s²

What is the perimeter of a square with side s?

P = 4s

What is the diagonal of a square with side s?

d = s√2

If a shape is enlarged by linear scale factor k, by what factor does its area change?

k²

If a shape is enlarged by linear scale factor k, by what factor does its volume change?

k³

What is the distance between two points (x₁, y₁) and (x₂, y₂)?

d = √[(x₂−x₁)² + (y₂−y₁)²]

What is the midpoint of a line segment between (x₁, y₁) and (x₂, y₂)?

M = ((x₁+x₂)/2 ; (y₁+y₂)/2)

What is the gradient of a line through (x₁, y₁) and (x₂, y₂)?

m = (y₂−y₁) ÷ (x₂−x₁)

What is the equation of a circle with centre (a, b) and radius r?

(x−a)² + (y−b)² = r²

What is the length of an arc with radius r and angle θ (in degrees)?

Arc = (θ/360) × 2πr

What is the area of a sector with radius r and angle θ (in degrees)?

Sector area = (θ/360) × πr²