Perimeter and Area

Common Formulas for Perimeter and Area Square Rectangle s l s w A = lw P = 4sP = 2l + 2w Perimeter and Area of Rectangle

1.Let l represent the unknown length. l = length of the rectangle. 2.Represent other unknowns in terms of l. there are no other unknowns 3.Write an equation that describes l the condition. 2w + 2l = P 2(10) + 2l = l =125 Example : A rectangle has a width of 10 inches and a perimeter of 125 inches. Find the length Perimeter of Rectangle

4.Solve the equation and answer the question l = 125 2l = 105 l = 52.5 The length of the rectangle is 52.5 inches. 5.Check the solution in the original problem. The perimeter of a rectangle that is 10 inches by 52.5 inches is 125 inches. 2(10) + 2(52.5) = 125 Example Continued: A rectangle has a width of 10 inches and a perimeter of 125 inches. Find the length. Perimeter of a Rectangle

Common Formulas for Area Triangle Trapezoid b h b a Area of Triangle and Trapezoid

Formulas for Circles r The Circle The circumference of a circle is a measure of length. The circumference of a circle is the distance around it, or its perimeter.

Example : Find the area and circumference of a circle with a radius of 5 inches. Area and Circumference of Circle

Common Formulas for Volume Cube Rectangular Solid Volume of a Cube and a Rectangular Solid

Common Formulas for Volume Circular Cylinder Sphere Volume of a Cylinder and a Sphere

Cone Volume of a Cone

Example : Find the volume of a cylinder that has a height of 4 feet and a radius of 5 feet. Volume of a Cylinder

Application problem: Area of a CircleSOLUTION Which one of the following is a better buy: a large pizza with a 16 inch diameter for $12.00 or two small pizzas, each with a 10 inch diameter, for $12.00? STEP 1: Since the cost is the same, we must just determine which has greatest area – the one big pizza or the two small ones. STEP 2: Find the area of the big pizza. The diameter is 16, so the radius is 8. The area of the big pizza is then: A = which is approximately 201 square inches.

Application, continuedCONTINUED Now we must find the area of each of the two smaller pizzas. A = which is approximately 78.5 square inches for each smaller pizza. We would have two of these, so the total area would be around 157 square inches. CONCLUSION: the best buy is the one large pizza! SO… when you are considering how big a pizza is – don’t just consider the radius. Consider the square of the radius! And that’s why one sixteen inch pizza would be bigger than two eight inch ones. It’s even bigger than two ten inch ones as we discovered above.