Measurement

Introduction There are many different ways that measurement is used in the real world. When you stand on a scale to see how much you weigh, you are measuring. Here are a few fact about Mississippi and the Earth using measurement:  Woodall Mountain is the highest point in the state of Mississippi. This mountain rises 806 feet above sea level.  The area of Mississippi is about 125,444 km 2.  The circumference of the Earth is calculated to be about 25,000 miles.

Length To measure customary units in length, use an inch ruler for length of 1 foot or less, a yardstick for lengths of 3 feet or less, and a tape measure for longer lengths. To measure metric units of length, use a centimeter ruler for lengths up to 30 centimeters, a meter stick for lengths of 1 meter or less, and a tape measure for longer lengths.

Example—What is the measure of the long side of this rectangle to the nearest 1/16 inch? Step 1—Place the ruler beneath the rectangle. Align the 0-mark of the ruler with the left edge of the rectangle. Step 2—Read the mark on the ruler that aligns with the right edge of the rectangle. –The mark is 6 marks after the 3. –The length is 3 6/16 inches. Step 3—Write the length in simplest form. –3 6/16 = 3 3/8 The length of the long side of the rectangle is 3 3/8 inches.

Perimeter Perimeter measures the distance around the outside of a closed figure. To find the perimeter of a polygon, add the lengths of all the sides. To find the perimeter of a rectangle, you can use the following formula: P = 2l + 2w To find the perimeter of a regular polygon, multiply the length of a side times the number of sides.

Example—What is the perimeter of this rectangle? Use the formula: P = 2l + 2w Substitute the length and the width into the formula. Then compute. –P =( mm) + ( mm) –P = 55 mm mm = 87.5 mm The perimeter is 8.5 millimeters.

Composite Figure A composite figure is a figure composed of two or more figures. To determine the perimeter of a composite figure, measure the distance around the outside of the figure.

Example—What is the perimeter of the composite figure? 5 cm 3 cm 4 cm 4 cm 3 cm 5 cm Find the lengths of the missing sides. Then add the side lengths. Use the properties of congruent figures to find the missing measures. –The rectangle has a width of 4 cm. –The left side of the rectangle is 4 cm. Add the lengths of the sides. –5 cm + 3 cm + 4 cm + 4 cm + 5 cm + 3 cm + 4 cm + 4 cm = 32 cm The perimeter of the figure is 32 cm. 4 cm

Circumference Circumference is the distance around the outside of a circle. The circumference of a circle can be found if you know the length of either the radius or the diameter. The radius is a line segment of the center to any point on the circle. The diameter is a line segment with any two points on the circle that passes through the center. The diameter is twice the length of the radius. If you know the radius of a circle, you can use the formula C = 2πr to find the circumference. If you know the diameter, you can use the formula C = πd. π(pi) is the circumference divided by the diameter. The exact value of π has never been determined, but you can use either 3.14 or 3 1/7 as an approximate value.

Example—What is the approximate circumference of a circle with a radius of 7 centimeters? Use 3.14 for π. Use the formula for the circumference of a circle: C = 2πr. Substitute the value for the variable. Then multiply. –Substitute the value for the variable. Then multiply. –C ≈ ≈ The approximate circumference of the circle is cm.

Area Area measures the inside region of a closed figure. Area is measured in square units. A square unit is an area equal to that of a square whose sides are one unit long. For example, a square centimeter (cm²) is an area equal to that of a square whose sides are 1 cm long. To find the area of a rectangle, use the formula A = lw.

Example—A rectangular playground has a length of 35 yards and width of 25 yards. What is the area of the playground? Use the formula for the area of a rectangle: A = lw. –A = 35 yd 25 yd –A = 875 yd² The area of the playground is 875 yd².

Example—Lee’s property is 400 feet long by 200 feet wide. What is the area of Lee’s property? Use the formula for the area of a square: A = s². –A = 400 ft 200 ft –A = 80,000 ft² The area of Lee’s property is 80,000 ft².