Question

vocabulary and core concept check

1. complete the sentence the perimeter of a square
2. writing what formulas can you use to find the area of

monitoring progress and modeling with
in exercises 3 - 6, classify the polygon by the number of sides. tell whether it is convex or concave. (see example 1.)
in exercises 7 - 12, find the perimeter of the polygon with the given vertices. (see example 2.)

Explanation:

Step1: Recall polygon - side number rules

A triangle has 3 sides, a quadrilateral has 4 sides, a pentagon has 5 sides, etc. A convex polygon has all interior angles less than 180 degrees and all diagonals are inside the polygon. A concave polygon has at least one interior angle greater than 180 degrees.

Step2: Analyze Exercise 3

The polygon in Exercise 3 has 4 sides. Since it has an interior angle greater than 180 degrees, it is concave.

Step3: Analyze Exercise 4

The polygon in Exercise 4 has 3 sides, so it is a triangle. All triangles are convex as their interior angles sum to 180 degrees and there are no diagonals that can be outside the shape.

Step4: Analyze Exercise 5

The polygon in Exercise 5 has 5 sides, so it is a pentagon. Since all its interior angles are less than 180 degrees, it is convex.

Step5: Analyze Exercise 6

The polygon in Exercise 6 has 5 sides, so it is a pentagon. It has an interior angle greater than 180 degrees, so it is concave.

Answer:

1. 4 - sided, concave
2. 3 - sided, convex
3. 5 - sided, convex
4. 5 - sided, concave