3. Perimeters and Areas of Composite Figures
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The grid square has a side length of 1 unit.
Estimated Perimeter: about 24.6 units
Estimated Area: about 41.1 square units
We want to estimate the perimeter and the area of the shaded figure. We can do these things one at a time.
We can recall that a perimeter is the distance around the outside of a two-dimensional figure. We can approximate the perimeter of our composite figure by estimating the sum of all of its side lengths. Let's start by considering the given diagram!
Notice that our figure consists of a rectangle and a semicircle. First, we can mark the grid square lengths on the diagram. We can recall that each grid square length is 1 unit long. Let's do it!
We found that there are 12 grid square lengths around our figure. Let's calculate the total length of grid square length!
We found that the radius of the semicircle is 4 grid square lengths long. We can substitute 4 for r and 3.14 for π in our formula.
The arc is 12.56 units long. Finally, we can calculate the length of the perimeter by adding 12 units and 12.56 units.
The figure has the perimeter of about 24.6 units.
We want to estimate the area of the composite figure. First, we can calculate the number of grid squares in the rectangle part. We can start by calculating the number of squares!
We found that there are 16 squares with the area of 1 square unit each. Rectangle Area 16* 1 =16 The rectangle has the area of 16 square units. Notice that estimating the area of a semicircle with grid squares is not precise. In this case, we can recall the formula for the area of a semicircle. Semicircle Area 1/2π r^2 Finally, we can substitute 4 for r and 3.14 for π in our formula.
Substitute values
Calculate power
Multiply
1/b* a = a/b
Calculate quotient
The semicircle has the area of 25.12 square units. Finally, we can calculate the area of our composite figure by adding the estimated area of a rectangle and the area of a semicircle.
The figure has the area of about 41.1 square units.