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Illuminations: Square in a Pentagon
/uploadedImages/Brain_Teasers/BT37-big.jpg

Square in a Pentagon

The diagram above shows the top of a regular pentagon with the top of a square inscribed in it. The shapes share a vertex at the top, and the other two vertices of the square lie on the sides of the pentagon. If the diagram were continued to include the entire pentagon and the entire square, which shape would extend below the other?

In other words, does the whole square fit inside the pentagon, does the square protrude at the bottom, or do the square and pentagon meet at a single point?


Math Topics
Geometry
Middle School, High School
7th Grade, 8th Grade, 9th Grade, 10th Grade, 11th Grade, 12th Grade
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Problem and solution

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Organization

National Council of Teachers of Mathematics

Website URL

Type of Resource

Activity Sheet
PDF File

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Resource k12

Illuminations: Square in a Pentagon
/uploadedImages/Brain_Teasers/BT37-big.jpg

Square in a Pentagon

The diagram above shows the top of a regular pentagon with the top of a square inscribed in it. The shapes share a vertex at the top, and the other two vertices of the square lie on the sides of the pentagon. If the diagram were continued to include the entire pentagon and the entire square, which shape would extend below the other?

In other words, does the whole square fit inside the pentagon, does the square protrude at the bottom, or do the square and pentagon meet at a single point?

Math Topics
Geometry
Middle School, High School
7th Grade, 8th Grade, 9th Grade, 10th Grade, 11th Grade, 12th Grade
Descriptions of PDFs

Problem and solution

What are you looking for?

Organization

National Council of Teachers of Mathematics

Website URL

Type of Resource

Activity Sheet
PDF File

Assigned Categories