Section 9.3 Perimeter and Area

What You Will Learn Perimeter Area

Definitions The perimeter, P, of a two-dimensional figure is the sum of the lengths of the sides of the figure. The area, A, is the region within the boundaries of the figure.

Formulas Figure Perimeter Area Rectangle P = 2l + 2w A = lw Square P = 4s A = s2 Parallelogram P = 2b + 2w A = bh Triangle P = s1 + s2 + s3 Trapezoid P = s1 + s2 + b1 + b2

Formulas

Example 1: Sodding a Lacrosse Field Rob Marshall wishes to replace the grass (sod) on a lacrosse field. One pallet of Bethel Farms sod costs $175 and covers 450 square feet. If the area to be covered is a rectangle with a length of 330 feet and a width of 270 feet, determine a) The area to be covered with sod.

Example 1: Sodding a Lacrosse Field a) the area to be covered with sod. Solution A = l • w = 330 • 270 = 89,100 ft2

Example 1: Sodding a Lacrosse Field b) Determine how many pallets of sod Rob needs to purchase. Solution Rob needs 198 pallets of sod.

Example 1: Sodding a Lacrosse Field c) Determine the cost of the sod purchased. Solution The cost of 198 pallets of sod is 198 × $175, or $34,650.

Pythagorean Theorem The sum of the squares of the lengths of the legs of a right triangle equals the square of the length of the hypotenuse. leg2 + leg2 = hypotenuse2 Symbolically, if a and b represent the lengths of the legs and c represents the length of the hypotenuse (the side opposite the right angle), then a2 + b2 = c2 a b c

Example 2: Crossing a Moat The moat surrounding a castle is 18 ft wide and the wall by the moat of the castle is 24 ft high (see Figure). If an invading army wishes to use a ladder to cross the moat and reach the top of the wall, how long must the ladder be?

Example 2: Crossing a Moat Solution The ladder needs to be at least 30 ft long.

Circles A circle is a set of points equidistant from a fixed point called the center. A radius, r, of a circle is a line segment from the center of the circle to any point on the circle. A diameter, d, of a circle is a line segment through the center of the circle with both end points on the circle. r d circumference

Circles The circumference is the length of the simple closed curve that forms the circle. r d circumference

Example 4: Determining the Shaded Area Determine the shaded area. Use the π key on your calculator and round your answer to the nearest hundredth.

Example 4: Determining the Shaded Area Solution Height of parallelogram is diameter of circle: 4 ft

Example 4: Determining the Shaded Area Solution Area of parallelogram = bh = 10 • 4 = 40 ft2 Area of circle = πr2 = π(2)2 = 4π ≈ 12.57 ft2

Example 4: Determining the Shaded Area Solution Area of shaded region = Area of parallelogram – Area of circle Area of shaded region ≈ 40 – 12.57 Area of shaded region ≈ 27.43 ft2