Lesson 15
Decomposing Bases for Area
Problem 1
You find a crystal in the shape of a prism. Find the volume of the crystal.
The point \(B\) is directly underneath point \(E\), and the following lengths are known:
- From \(A\) to \(B\): 2 mm
- From \(B\) to \(C\): 3 mm
- From \(A\) to \(F\): 6 mm
- From \(B\) to \(E\): 10 mm
- From \(C\) to \(D\): 7 mm
- From \(A\) to \(G\): 4 mm
![An irregular pentagonal prism with base A, F, E, D, C. Segment A, G indicates the height of the prism. Point B lies between A and C.](https://cms-im.s3.amazonaws.com/wauRgHo3jjdirSvGxuDHPCkR?response-content-disposition=inline%3B%20filename%3D%227-7.6.C.PP.Image.06.png%22%3B%20filename%2A%3DUTF-8%27%277-7.6.C.PP.Image.06.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240718%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240718T034303Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=0e4617483bfac796db69410ae3f9e9374b5894a98c0abe50aa67b9d864fff0d6)
Solution
Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.
Problem 2
A rectangular prism with dimensions 5 inches by 13 inches by 10 inches was cut to leave a piece as shown in the image. What is the volume of this piece? What is the volume of the other piece not pictured?
![A right trapezoidal prism. Each base is a trapezoid with bases 13 inches and 1 inch, height 5 inches. The prism has height 10 inches.](https://cms-im.s3.amazonaws.com/pcSxM4jR9ZY3h51jxUssoQcs?response-content-disposition=inline%3B%20filename%3D%227-7.6.C.PP.Image.05.png%22%3B%20filename%2A%3DUTF-8%27%277-7.6.C.PP.Image.05.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240718%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240718T034303Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=0e8b3e6b8339ae272c65641f844bf5163bfb749d6a43227a08054f4b918eeaf5)
Solution
Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.
Problem 3
A triangle has one side that is 7 cm long and another side that is 3 cm long.
-
Sketch this triangle and label your sketch with the given measures. (If you are stuck, try using a compass or cutting some straws to these two lengths.)
-
Draw one more triangle with these measures that is not identical to your first triangle.
- Explain how you can tell they are not identical.
Solution
Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.
(From Unit 1, Lesson 17.)Problem 4
Select all equations that represent a relationship between angles in the figure.
![Three points intersect to form 6 lines. Clockwise, the angles measure b degrees, 30 degrees, 90 degrees, a, degrees, c degrees, blank.](https://cms-im.s3.amazonaws.com/inij2gqPDAFmmhmEdBrfdbr8?response-content-disposition=inline%3B%20filename%3D%227-7.7.A4.new.PP.04.png%22%3B%20filename%2A%3DUTF-8%27%277-7.7.A4.new.PP.04.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240718%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240718T034303Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=1e87a75089a499a1e4c73b7778923213769deb7e14b01dd4c155f0ea8e2232f4)
\(90-30=b\)
\(30+b=a+c\)
\(a+c+30+b=180\)
\(a=30\)
\(a=c=30\)
\(90+a+c=180\)
Solution
Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.
(From Unit 1, Lesson 12.)