a ² + b ² = c ²

Area and Perimeter of Triangle

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

Area of Parallelogram

Area of Trapezoid

Circumference of a Circle and Area of a Circular Region

Arclength and Area of a Circular Sector

Area = (1/2) *r ² * t

where t is the central angle in RADIANS.

Volume and Surface Area of a Rectangular Solid

Volume and Surface Area of a Sphere

Volume and Surface Area of a Right Circular Cylinder

Volume and Surface Area of a Right Circular Cone

Questions and Answers For Geometry Formulas

1. A rectangle has a perimeter of 320 meters and its length L is 3 times its width W. Find the dimensions W and L, and the area of the rectangle.

Solution and answer:

• Use the formula of the perimeter to write.
  2 L + 2 W = 320
• We now rewrite the statement “its length L is 3 times its width W” into a mathematical equation as follows:
  L = 3 W
• We substitute L in the equation 2 L + 2 W = 320 by 3 W.
  2(3 W) + 2 W = 320
• Expand and group like terms.
  8 W = 320
• Solve for W.
  W = 40 meters
• Use the equation L = 3 W to find L.
  L = 3 W = 120 meters
• Use the formula of the area.
  Area = L W = 120 * 40 = 4800 meters ²

2. The perimeter of a rectangle is 50 feet and its area is 150 feet ². Find the length L and the width W of the rectangle, such that L > W.

Solution and answer:

• Use the formula of the perimeter to write
  2 L + 2 W = 50
• and the formula of the area to write
  L W = 150
• Divide all terms in the equation 2 L + 2 W = 50 by 2 to obtain
  L + W = 25
• Solve the above for W
  W = 25 – L
• Substitute W by 25 – L in the equation L W = 150
  L(25 – L) = 150
• Expand the above equation and rewrite with right term equal to zero.
  -L ² + 25 L – 150 = 0

Sources: Wikipedia