SMARTWAY CLASSES

Right Triangle and Pythagora's theorem

Pythagora's theorem: The two sides a and b of a right triangle and the hypotenuse c are related by

a ² + b ² = c ² 

Area and Perimeter of Triangle

Perimeter = a + b + c

There are several formulas for the area.

If the base b and the corresponding height h are known, we use the formula

Area = (1 / 2) * b * h.
If two sides and the angle between them are known, we use one of the formulas, depending on which side and which angle are known

Area = (1 / 2)* b * c sin A 

Area = (1 / 2)* a * c sin B 

Area = (1 / 2)* a * b sin C .
If all three sides are known, we may use Heron's formula for the area.

Area = sqrt [ s(s - a)(s - b)(s - c) ] , where s = (a + b + c)/2.

Area and Perimeter of Rectangle

Perimeter = 2L + 2W

Area = L * W

Area of Parallelogram

Area = b * h

Area of Trapezoid

Area = (1 / 2)(a + b) * h

Circumference of a Circle and Area of a Circular Region

Circumference = 2*Pi*r

Area = Pi*r ²

Arclength and Area of a Circular Sector

Arclength: s = r*t

Area = (1/2) *r ² * t

where t is the central angle in RADIANS.

Volume and Surface Area of a Rectangular Solid

Volume = L*W*H

Surface Area = 2(L*W + H*W + H*L)

Volume and Surface Area of a Sphere

Volume = (4/3)* Pi * r ³

Surface Area = 4 * Pi * r ²

Volume and Surface Area of a Right Circular Cylinder

Volume = Pi * r ² * h

Surface Area = 2 * Pi * r * h

Volume and Surface Area of a Right Circular Cone

Volume = (1/3)* Pi * r ² * h

Surface Area = Pi * r * sqrt (r ² + h ²)