1. Pre-Algebra Area: Parallelograms Lesson 10-1

2. Pre-Algebra Area: Parallelograms Find the area of the rectangle. Lesson 10-1 Step 1:Change the units so that they are the same. 150 cm = 1.5 mChange 150 centimeters to meters. Step 2:Find the area. A = bhUse the formula for area of a rectangle. = (4)(1.5)Replace b and h with the dimensions 4 and 1.5. = 6Simplify. The area of the rectangle is 6 m 2.

3. Pre-Algebra Area: Parallelograms Find the area of each parallelogram. Lesson 10-1 a.b. A = bharea formula = (8)(2)Substitute. = 16Simplify. The area is 16 m 2.The area is 15 in. 2. A = bh = (2.5)(6) = 15

4. Pre-Algebra Area: Triangles and Trapezoids Lesson 10-2

5. Pre-Algebra Area: Triangles and Trapezoids Find the area of the triangle. Lesson 10-2 The area is 39 in. 2. A = bhUse the formula for area of a triangle. 1212 = 13 6Replace b with 13 and h with 6. 1212 = 39Simplify.

6. Pre-Algebra Area: Triangles and Trapezoids Find the area of the figure. Lesson 10-2 Add to find the total: 450 + 1,350 = 1,800. Area of triangle A = bh 1212 = 45 20 1212 = 450 Area of rectangle A = bh = 45 30 = 1,350 The area of the figure is 1,800 cm 2.

7. Pre-Algebra Area: Triangles and Trapezoids Suppose that, through the years, a layer of silt and mud settled in the bottom of the Erie Canal. Below is the resulting cross section of the canal. Find the area of the trapezoidal cross section. Lesson 10-2 The area of the cross section is 106.5 ft 2. A = h(b 1 + b 2 )Use the formula for the area of a trapezoid. 1212 A = 3(31 + 40)Replace h with 3, b 1 with 31, and b 2 with 40. 1212 = 3(71)Simplify. 1212 = 213 1212 = 106.5

8. Pre-Algebra Area: Circles Lesson 10-3

9. Pre-Algebra Area: Circles Find the exact area of a circle with diameter 20 in. Lesson 10-3 A = r 2 = (10) 2 r = d; r = 10 1212 = 100Simplify. The area is 100 in. 2.

10. Pre-Algebra Area: Circles A TV station’s weather radar can detect precipitation in a circular region having a diameter of 100 mi. Find the area of the region. Lesson 10-3 A = r 2 The area of the region is about 7,850 mi 2. = (50) 2 r = d; r = 50 1212 = 2,500exact area (2,500)(3.14)Use 3.14 for. = 7,850approximate area

11. Pre-Algebra Area: Circles A pound of grass seed covers approximately 675 ft 2. Find the area of the lawn below. Then find the number of bags of grass seed you need to buy to cover the lawn. Grass seed comes in 3-lb bags. Lesson 10-3 Area of region that is one fourth of a circle: area of circle = r 2 area of quarter circle = r 2 A (3.14)(15) 2 Replace with 3.14 and r with 15. = 176.625 ft 2 1414 1414

12. Pre-Algebra Area: Circles (continued) Lesson 10-3 Area of region that is a rectangle: area of rectangle = bh A = 45 25Replace b with 45 and h with 25. = 1,125 The area of the lawn is about 177 ft 2 + 1,125 ft 2 = 1,302 ft 2. You need to buy one 3-lb bag of grass seed. 1,302 ÷ 675 1.93Divide to find the number of pounds of seed.

13. Pre-Algebra Space Figures Lesson 10-4

14. Pre-Algebra Space Figures Describe the bases and name the figure. Lesson 10-4 The bases are circles. The figure is a cylinder.

15. Pre-Algebra Space Figures Name the space figure you can form from the net. Lesson 10-4 With two hexagonal bases and rectangular sides, you can form a hexagonal prism.

16. Pre-Algebra Surface Area: Prisms and Cylinders Lesson 10-5

17. Pre-Algebra Surface Area: Prisms and Cylinders Find the surface area of the rectangular prism using a net. Lesson 10-5 60 + 60 + 150 + 90 + 150 + 90 = 600 Add the areas. The surface area is 600 cm 2. Draw and label a net. Find the area of each rectangle in the net.

18. Pre-Algebra Surface Area: Prisms and Cylinders Find the surface area of the rectangular prism. Lesson 10-5 The surface area of the rectangular prism is 500 in. 2. Step 1:Find the lateral area. L.A. = ph Use the formula for lateral area. = (5 + 6 + 5 + 6)20 p = 5 + 6 + 5 + 6 and h = 20 = 440 Step 2:Find the surface area. S.A. = L.A. + 2B Use the formula for surface area. = 440 + 2(5 6) L.A. = 440 and B = 5 6 = 440 + 60 = 500

19. Pre-Algebra Surface Area: Prisms and Cylinders Find the surface area of the cylindrical water tank. Lesson 10-5 The surface area of the water tank is about 1,156 ft 2. Step 1:Find the lateral area. L.A. = 2 rh Use the formula for lateral area. 2(3.14)(8)(15) 754 Step 2:Find the surface area. S.A. = L.A. + 2B Use the formula for surface area. = L.A. + 2( r 2 ) 754 + 2(3.14)(8) 2 1,156

20. Pre-Algebra Surface Area: Pyramids, Cones, and Spheres Lesson 10-6

21. Pre-Algebra Surface Area: Pyramids, Cones, and Spheres Find the surface area of the square pyramid. Lesson 10-6 The surface area of the pyramid is 105 m 2. Step 1: L.A. = p Use the formula for lateral area. 1212 = 20 8 = 80 p = 4(5) and = 8. 1212 Step 2: S.A. = L.A. + B Use the formula for surface area. = 80 + 5 2 Lateral area = 80 and B = 5 2. = 80 + 25 = 105

22. Pre-Algebra Step 1: L.A. = r Use the formula for lateral area. 3.14(3)(7) r = 3 and = 7. = 65.94 Surface Area: Pyramids, Cones, and Spheres Find the surface area of the cone. Lesson 10-6 The surface area of the cone is about 94 m 2. Step 2: S.A. = L.A. + B Use the formula for surface area. 65.94 + 3.14(3) 2 L.A. 65.94 and B = (3) 2. = 65.94 + 28.26 = 94.2

23. Pre-Algebra Surface Area: Pyramids, Cones, and Spheres Earth has an average radius of 3,963 mi. What is Earth’s approximate surface area to the nearest 1,000 mi 2 ? Assume that Earth is a sphere. Lesson 10-6 The surface area of Earth is about 197,259,000 mi 2. S.A. = 4 r 2 Use the formula for surface area. = 197,259,434.64Multiply. 197,259,000Round to nearest 1,000. 4(3.14)(3,963) 2 r 3,963

24. Pre-Algebra Volume: Prisms and Cylinders Lesson 10-7

25. Pre-Algebra Volume: Prisms and Cylinders Find the volume of the triangular prism. Lesson 10-7 The volume is 1,260 cm 3. V = BhUse the formula for volume. = 63 20 B = 9 14 = 63 cm 2 1212 = 1,260 Simplify.

26. Pre-Algebra Volume: Prisms and Cylinders Find the volume of the juice can, to the nearest cubic centimeter. Lesson 10-7 The volume is about 581 cm 3. V = Bh Use the formula for volume. V = r 2 h B = r 2 = 580.7744 Simplify. 3.14 3.4 2 16 Replace r with 3.4, and h with 16.

27. Pre-Algebra Volume: Pyramids, Cones, and Spheres Lesson 10-9

28. Pre-Algebra Volume: Pyramids, Cones, and Spheres Find the volume of the cone. Lesson 10-9 V = Bh Use the formula for volume. 1313 V = r 2 h B = r 2 1313 (3.14)(2) 2 (12) Replace r with 2 and h with 12. 1313 = 50.24 Simplify. The volume of the cone is about 50 in. 3.

29. Pre-Algebra Volume: Pyramids, Cones, and Spheres Find the volume of the square pyramid. Lesson 10-9 The volume of the pyramid is 256 in. 3. V = Bh Use the formula for volume. 1313 V = s 2 h B = s 2 1313 = (8) 2 (12) Replace s with 8 and h with 12. 1313 = 256 Simplify.

30. Pre-Algebra Volume: Pyramids, Cones, and Spheres Earth has an average radius of 3,963 mi. What is Earth’s approximate volume to the nearest 1,000,000 mi 3 ? Assume that Earth is a sphere. Lesson 10-9 The volume of the Earth is about 260,580,000,000 mi 3. V = r 3 Use the volume formula. 4343 (3.14)(3,963) 3 Replace r with 3,963. 4343 260,579,713,159Simplify. Additional Examples