To review these concepts, go to Polygons and Triangles Study Guide.

**Polygons and Triangles Practice Questions**

**Practice**

Determine which of the following figures are polygons, and name them. Why aren't the others polygons?

Find the perimeter of each polygon.

**Word Problems**

- Maryellen has cleared a 10-foot by 6-foot rectangular plot of ground for her herb garden. She must completely enclose it with a chain-link fence to keep her dog out. How many feet of fencing does she need, excluding the 3-foot gate at the south end of the garden?
- Terri plans to hang a wallpaper border along the top of each wall in her square dressing room. Wallpaper border is sold only in 12-foot strips. If each wall is 8 feet long, how many strips should she buy?

Name the triangle, the marked angle, and the side opposite the marked angle.

Classify each triangle as equilateral, isosceles, scalene, or right. Remember, some triangles have more than one classification.

- The base of a triangle is 14 feet long, and the height is 5 feet. How many square feet of area is the triangle?
- If a triangle with 100 square feet of area has a base that is 20 feet long, how tall is the triangle?

Find the area of the triangles below.

Find the missing angles and identify the longest and shortest sides

Find the perimeter and area of each triangle. **Hint**: Use the Pythagorean theorem.

#### Word Problems

- Erin is flying a kite. She knows that 260 feet of the kite string has been let out. Also, a friend is 240 feet away and standing directly underneath the kite. How high off the ground is the kite?
- What is the length of a side of an equilateral triangle that has the same perimeter as the triangle shown at right?

**Solutions**

- yes, square
- no, not a closed figure
- no, one side is curved
- yes, triangle
- no, line segments cross
- no, not flat (it's three-dimensional)
- 14 in.
- 20 in.
- 16 in.
- 29 ft. (The perimeter is 32 feet; subtract 3 feet for the gate.)
- 3 strips (There will be 4 feet of border left over.)
- The triangle is named ABC. The marked angle is B or ABC or CBA. The opposite side is .
- The triangle is named XYZ. The marked angle is Y or XYZ or ZYX. The opposite side is .
- right, scalene
- equilateral, isosceles
- isosceles
- isosceles, right
- 35 square feet
- 10 feet
- 12 square units
- 3 square units
- 18 square units
- 24 square units
- The measure of C (also called ACB or BCA) is 40°. The longest side is , and the shortest side is .
- J = L = 70°. Longest sides are and . Shortest side is .
- Y = 45°. Longest side is . Shortest sides are and .
- N = 80°. Longest side is. Shortest side is .
- The perimeter is 120, and the area is 600.
- The perimeter is 36, and the area is 54.
- The perimeter is 30, and the area is 30.
- The perimeter is 18, and the area is 12.
- 100 feet
- 4 units. The hypotenuse of the triangle shown is 5, making its perimeter 12. Since all three sides of an equilateral triangle are the same length, the length of each side is 4 units (12 ÷ 3 = 4).

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