NooliArea of a square
A = s^2, where s is the side length
A square with side 5 cm has area 5^2 = 25 cm².
Area formulas
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5 of 1212 of 12Area of a rectangle
A = l \cdot w, where l is the length and w the width
A rectangle 4 m by 3 m has area 4 \cdot 3 = 12 m².
Area of a triangle
A = \frac{1}{2} b h, where b is the base and h the height
A triangle with base 6 cm and height 4 cm has area \frac{1}{2} \cdot 6 \cdot 4 = 12 cm².
Area of a parallelogram
A = b h, where b is the base and h the height
A parallelogram with base 8 cm and height 5 cm has area 8 \cdot 5 = 40 cm².
Area of a trapezoid
A = \frac{1}{2}(b_1 + b_2) h, where b_1, b_2 are the parallel bases and h the height
A trapezoid with bases 6 cm and 10 cm and height 4 cm has area \frac{1}{2}(6+10) \cdot 4 = 32 cm².
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Area of a circle
A = \pi r^2, where r is the radius
A circle with radius 3 cm has area \pi \cdot 3^2 = 9\pi cm².
Area of an ellipse
A = \pi a b, where a and b are the semi-major and semi-minor axes
An ellipse with semi-axes 4 cm and 3 cm has area \pi \cdot 4 \cdot 3 = 12\pi cm².
Area of a regular polygon
A = \frac{1}{2} P a, where P is the perimeter and a the apothem
A regular hexagon with perimeter 24 cm and apothem 3.46 cm has area \frac{1}{2} \cdot 24 \cdot 3.46 \approx 41.5 cm².
Area of a circle sector
A = \frac{\theta}{360^\circ} \pi r^2 (degrees) or A = \frac{1}{2} r^2 \theta (radians)
A 60° sector of a circle of radius 6 cm has area \frac{60}{360} \pi \cdot 6^2 = 6\pi cm².
Area of a rhombus
A = \frac{1}{2} d_1 d_2, where d_1, d_2 are the diagonals
A rhombus with diagonals 6 cm and 8 cm has area \frac{1}{2} \cdot 6 \cdot 8 = 24 cm².
Area of a triangle (Heron's formula)
A = \sqrt{s(s-a)(s-b)(s-c)}, where a, b, c are the sides and s = \frac{a+b+c}{2} the semiperimeter
A triangle with sides 3, 4, 5 cm has s = 6 and area \sqrt{6 \cdot 3 \cdot 2 \cdot 1} = 6 cm².
Area of a triangle with two sides and the included angle
A = \frac{1}{2} a b \sin C, where a, b are two sides and C the angle between them
Two sides of 5 cm and 7 cm with a 30° angle between them give area \frac{1}{2} \cdot 5 \cdot 7 \cdot \sin 30^\circ = 8.75 cm².