Measuring Perimeter : Measuring Perimeter in 4th grade & Area Perimeter versus Area of Rectangles : Perimeter versus Area of Rectangles Perimeter measures the distance around. To calculate the perimeter, add up the measure of all sides.
P = length + length + width + width
P = l + l + w + w
P = (length + length) + (width + width)
P = 2(length) + 2(width)
P = 2l + 2w Area measures the space inside. To calculate the area, simply multiply the length times the width.
A = length x width
A = l x w You must be able to recognize the 2 ways to write the equation for perimeter. Perimeter versus Area of Rectangles : Perimeter versus Area of Rectangles Perimeter is a linear measurement, meaning that it is a “line,” and it has only 1 dimension. Area is a measure of two dimensions. Therefore, the units of measure for area are written as square units or as units2 Examples:
P = 16 feet
P = 24 cm Examples:
A = 20 square feet or 16 ft2
A = 32 square cm or 24 cm2 Perimeter versus Area : Perimeter versus Area Two rectangles can have the same area and different perimeters. Here’s an example: 2 units 20 units P = 44 units A = 40 units2 4 units 10 units P = 28 units
A = 40 units2 …There will probably be some kind of question that tests your general understanding of this fact. Perimeter versus Area : Perimeter versus Area On the other hand, two rectangles can have the same perimeter and different areas. 13 units 2 units P = 30 units A = 26 units2 7 units 8 units P = 30 units
A = 56 units2 …There will probably be some kind of question that tests your general understanding of this fact. Perimeter of polygons : Perimeter of polygons that are made up of rectangles or squares… 2 2 5 14 Perimeter can’t be calculated until you figure out the length of the unmarked sides: A B Length A = 14 – (2+2) = 10 units
Length B = 5 units because the opposite side of the rectangle = 5
Length C = 4 units because the opposite side = 4 C Now add up all of the sides. There are 8 sides, so there should be 8 values in the equation! Starting at side A, and adding clockwise, here are the measurements:
P = 10 + 5 + 14 + 5 + 2 + 4 + 2 + 4
P = 48 units 4 Area of polygons : Area of polygons that are made up of rectangles or squares… Area can’t be calculated until you figure out how many rectangles or squares make up the polygon. In this example, there are two rectangles stuck together. We can see their length and their width. Calculate the area of each rectangle, and add the two areas together:
A = (L x W) of the smaller rectangle A = (L x W) of the bigger rectangle Then Total A = A + A. We can write one equation for all of these steps:
Total A = (4 x 2) + (14 x 5)
Total A = 8 + 70
Total A = 78 sq. units or 78 units2 Perimeter versus Areain Word Problems : Perimeter versus Areain Word Problems Look for key words that tell you which one to calculate. PERIMETER: AREA: A farmer is putting up a fence around a field that is 100 feet by 200 feet. How much fencing will he need?
A decorator wants to glue a border around the ceiling of a bedroom that is 12 feet by 12 feet. How much border will she need? A farmer is covering a field that is 100 feet by 200 feet with fertilizer. How much fertilizer will he need?
A decorator wants to install new carpeting in the living room, which is 18 ft x 15 ft. How much carpet will she need? If there isn’t a key word, then you must draw a picture or visualize the situation. 15 18