Unit 7 Polygons and Quadrilaterals is an important part of mathematics that deals with shapes and angles. It is important for students to understand the concepts of this unit and be able to answer homework questions. Homework 1 of this unit can be difficult for some students, so understanding the answers to the questions can be helpful.

## Types of Polygons and Quadrilaterals

Polygons are shapes with three or more sides. They can be either convex or concave. Quadrilaterals are shapes with four sides and also can be convex or concave. Examples of convex polygons are triangles, squares, pentagons, hexagons, and octagons. Examples of concave polygons are pentagons with one or more sides that are not straight, and hexagons with one or more sides that are not straight. Examples of convex quadrilaterals are squares, rectangles, rhombuses, and trapezoids. Examples of concave quadrilaterals are quadrilaterals with one or more sides that are not straight.

## Angles of Polygons and Quadrilaterals

The angles of polygons and quadrilaterals are important to understand in order to answer homework questions. The sum of the interior angles of a polygon is (n-2)180, where n is the number of sides. For example, the sum of the interior angles of a triangle is 180, the sum of the interior angles of a square is 360, and the sum of the interior angles of a pentagon is 540. The sum of the interior angles of a quadrilateral is 360. All the angles of a square are right angles, and all the angles of a rectangle are right angles.

## Properties of Polygons and Quadrilaterals

Polygons and quadrilaterals have certain properties that are important to understand in order to answer homework questions. The diagonals of a polygon are lines that connect two non-adjacent vertices. The diagonals of a quadrilateral are lines that connect two non-adjacent vertices, and they can be either equal or unequal. The area of a polygon is the sum of the areas of its individual triangles, and the area of a quadrilateral is the product of its base and height. The perimeter of a polygon is the sum of the lengths of its sides, and the perimeter of a quadrilateral is the sum of the lengths of its four sides.

## Questions from Homework 1 and Answers

The questions from Homework 1 of Unit 7 Polygons and Quadrilaterals are as follows: What is the sum of the interior angles of a pentagon? What is the area of a square with a side length of 6? What is the perimeter of a rectangle with a length of 8 and a width of 3? What type of quadrilateral is a rhombus? The answers to these questions are 540, 36, 22, and a convex quadrilateral.

Unit 7 Polygons and Quadrilaterals is an important part of mathematics that deals with shapes and angles. Understanding the types of polygons and quadrilaterals, the angles of polygons and quadrilaterals, and the properties of polygons and quadrilaterals can be helpful to answer homework questions. The answers to the questions from Homework 1 of Unit 7 Polygons and Quadrilaterals are 540, 36, 22, and a convex quadrilateral.