Find the area of each shaded region. Show or explain your reasoning.

Name: Problem 2, Chapter 1: Grade 6 Mathematics: Open Up Resources, Common Core State Standards Edition
Uploaded: 2021-12-30T21:55:07-08:00
Duration: 2 min 39 s
Channel: Julie Silva
Description: Find the area of each shaded region. Show or explain your reasoning.

Find the area of each shaded region. Show or explain your...

Key Concepts

Decomposition Strategy

Decomposition refers to the method of breaking down a complex geometric figure into simpler, non-overlapping parts. This technique simplifies the process of calculating the total area by making it possible to use standard geometric formulas on manageable segments and recombine the results to solve for the area of the original figure.

Area Calculation

Area calculation involves determining the number of square units that cover a two-dimensional shape. This process requires knowledge of specific formulas for various shapes, such as the area of rectangles, triangles, and circles, and forms the fundamental basis of solving many problems in geometry.

Composite Figures

Composite figures are shapes made up of several simpler shapes. When faced with a composite figure, the strategy is to partition it into recognizable basic shapes whose areas can be calculated individually, and then either summed or subtracted, depending on how the shapes combine or overlap.

Transcript

00:01 So in this problem, we want to find the area for each of these shapes.

00:03 So why don't we start with shape a? so notice that we have a little square at the top and then a rectangle below.

00:11 So to find the whole area, what we're going to do first is find the area of the two different sections.

00:15 So to find the area at the top, we're going to multiply the height, which is two, by the length, which is two.

00:21 So that would be two times two, which is four.

00:24 Then we're going to find the area of the bottom rectangle.

00:28 We'll notice that this is six and this is six.

00:30 So we would do 6 times 6, which is 36.

00:34 So now to find the total, we're going to add them together.

00:37 Well, 4 plus 36 is equal to 40.

00:40 So notice we have centimeters here, so it'll be square centimeters.

00:43 So that's the answer to the part a.

00:45 Now, for part b, notice we have this rectangle on the outside, and we have this kind of cut out missing space in between.

00:56 So to find the shaded area, what we can do is find the area of the whole rectangle, including the missing piece, and subtract that by the area of the missing piece.

01:05 Well, to find the area of the whole, we're going to take the length, which is 8, and multiply it by the height, which is 5, and we're going to subtract the area of the missing piece, whose length is 3 and whose height is 2.

01:16 Well, 8 times 5 is equal to 40, 3 times 2 is 6, and 40 minus 6 is 34...

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