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Nesterboy [21]
3 years ago
11

A pentagonal prism is cut by a plane perpendicular to the base. What is the shape of the cross section that is formed?

Mathematics
1 answer:
rewona [7]3 years ago
5 0

Answer: A rectangle

Note: I am a bit confused between A), B), and C), but the answer I am going for is C).

Step-by-step explanation:

By definition, a cross-section is the intersection of a plane and a body of three dimensions.

A pentagonal prism has a pentagon as its base. and its lateral faces are rectangles.

If a plane perpendicular cuts the pentagonal prism to the base, this means that the plane is parallel to lateral faces, then, the shape of the cross-section that is formed is also a rectangle.

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Answer:

(9.37, 17.7) ; (14.10, 19.42); (20.8, 22.3)

Step-by-step explanation:

For the first picture :

The missing angle :

180 - (32 + 90)

180 - (122) = 58°

To obtain the length of side x:

From ptthagoras:

Tan58° = opposite / Adjacent

1.6003345 = 15 / x

x = 15 / 1.6003345

= 9.37

y = sqrt(15^2 + 9.37^2)

y = sqrt(312.7969)

y = 17.7m

2)

Missing angle :

From ptthagoras :

Sin54° = opposite / hypotenus

0.8090169 = y/ 24

y = 0.8090169 * 24

y = 19.42

x = sqrt(24^2 - 19.42^2)

x = sqrt(198.8636)

x = 14.10

3)

Sin21° = opposite / hypotenus

0.3583679 = 8 /y

y = 8 / 0.3583679

y = 22.3

x = sqrt(22.3^2 - 8^2)

x = sqrt(433.29)

x = 20.8

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3 years ago
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