In each of the following problems draw a right triangle for each problem then substitute values and solve.

1. A suitcase measures 22 inches long and 16 inches high. What is the diagonal length of the suitcase to the nearest foot?

2. A right triangle has a hypotenuse of 25 and a leg of 7. What is the measure of the other leg?

3. Two joggers run 6 miles north then 9 miles west. What is the shortest distance to the nearest mile that they must travel to return to the starting point?

4. A 104-foot ladder is leaned against a wall. If the base of the ladder is 40 ft from the wall, how up the wall will the ladder reach?

5. To avoid the pong Fred must walk 10 meters south and 24 meters east> To the nearest meter, how many meters would be saved if it were possible to walk through the pond?

6. A triangle has a width of 15 inches and a diagonal of 17 inches. Find the length of the rectangle in inches.

7. Slanted sides of a tent are 11 feet long each and the bottom of the tent is 12 feet across. What is the tallest point of the tent?

8. A 12-foot pole casts a shadow of 16 feet. What is the distance between the end of the shadow and the top of the pole?

9. Harold rides his bike 33 km south and then 56 km west. How far is the shortest distance from his starting point?

Calculate the area of each of the polygons with the following dimensions.

1. Triangles

1. 1. B = 4in, H = 5in
2. 1. B = 6ft, H= 10ft
   2. B = 12m, H = 15m
   3. Application: Sandy is making tablecloths in the shape of triangles. She needs to make two triangle tablecloths for one table. The triangles have base of 2 ft and a height of 4 ft. What is the total area of the triangle tablecloths for one table?

2. Parallelogram (H = height) and (B = base)

1. 1. H = 9in, B = 6in
2. 1. H = 5 ft, B = 2ft
3. 1. H = 7yds, B = 3yds
   2. Application: If a parallelogram has a base of 13 mm and an area of 78 mm2 what is the height?

Hint: Use the formula. Substitute the given values and then solve as an equation.

3. Rectangle (L = length) and (w = width)

1. 1. rect. DKIF with L = 8 ft and w = 6 ft
2. 1. rect. AOPU with L = 13 ft and w = 5 ft
   2. Application: Charles is paining the den. Two walls are 9 ft high and 15 ft long. The other two walls are 8 ft high and 10 ft long. Charles bought one gallon of paint that will cover 440 square feet of wall space. Does he have enough paint? Explain.

4. Rhombus ( d1 = diagonal 1) (d2 = diagonal 2)

1. 1. rhombus with d1 = 12 yds and d2 = 12 yds
2. 1. rhombus with d1 = 10 ft and d2 = 25 ft
3. 1. rhombus with d1 = 16 in and d2 = 22 in
   2. Application: a rhombus as an area of 72 ft and the product of the diagonals is 144. What is the length of each diagonal?

5. Trapezoid ( b1 = base 1) (b2 = base 2) (H = height)

1. 1. b1 = 6 ft, b2 = 7 ft, H = 10 ft
2. 1. b1 = 5 yds, b2 = 8 yds, H = 4 yds
   2. c. b1 = 9 in, b2 = 11 in, H = 13 in
   3. d. Application: The two bases of a trapezoid = 16 km and its area = 32 km2. What is its height?

Hint: Use the formula. Substitute the given values and then solve as an equation.

Calculate the surface area of each pyramid with the following values. (P = perimeter, b = one side of the base, s=side, h=height). Number of sides is given in each problem. The first two have hints to let you know what the shape of the base is…..

1. P = 12 ft, s = 4 ft, b = 4 ft, h=2 ft, 3 sides (base is a triangle)

2. b = 4 in, P = 16 in, s = 12, 4 sides (base is a square)

3. P = 48 m, b = 12 m, s=12, 4 sides

4. P = 45 yds, b = 15 yds, s=15, h=12, 3 sides

5. b = 6 ft, P = 24 ft, s=6, 4 sides

6. P = 15 ft, b = 5 ft, s=5 ft, h= 4, 3 sides

7. b = 4 in, P = 16 in, s=11, 4 sides

8. P = 40 m, b = 10 m, s=10, 4 sides

9. P = 45 yds, b = 15 yds, s=10, h=8, 3 sides

10. b = 16 ft, P = 64 ft, s=8, 4 sides

11. b = 5 ft, P = 20 ft, s=7, 4 sides

12. P = 45 ft, b = 15 ft, s=10, h=8, 3 sides

13. b = 13 in, P = 52 in, s=11, 4 sides

14. P = 28 m, b = 7 m, s=8, 4 sides

15. P = 27 yds, b = 9 yds, s=30, h=25, 3 sides