Area of Parallelograms (pages )
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1 A Area of Parallelograms (pages ) A parallelogram is a quadrilateral with two pairs of parallel sides. The base is any one of the sides and the height is the shortest distance (the length of a perpendicular segment) from the base to the opposite side. Finding the The area A of a parallelogram equals the product Area of a of its base b and height h. Parallelogram A bh h b A Find the area of the parallelogram. Multiply the length of the base of the parallelogram (4 in.) and the height drawn to that base (5 in.). A bh A 4(5) 20 in 2 b = 4 in. h = 5 in. The area of a parallelogram is 30 square inches. The base is 0 inches long. What is the height? A bh 30 0h Substitute the values you know. h The height is 3 inches.. Find the area (to the nearest tenth) of 2. Find the base of a parallelogram that has a parallelogram that is 6 centimeters a height of 7 centimeters and an area of wide and 5.2 centimeters high. 56 square centimeters. HINT: Use the formula and then round. HINT: Write the formula, substitute values, and solve for b. Find the area of each parallelogram cm 6 cm 6. What is the area of a parallelogram that is 5 centimeters wide and 8 centimeters high? Puzzles Kai has a puzzle that is a parallelogram. It is 30 centimeters long and 22 centimeters high. What is the area of the puzzle? 2 m 8 m 3 ft 4 ft Standardized Test Practice If a parallelogram has an area of 42 square centimeters and its height is 6 centimeters, how long is its base? A 6 cm 7 cm C 5 cm D 8 cm Answers:. 7 in cm 24 cm 2 6 m ft cm cm 2 98 Mathematics: Applications and Concepts, Course
2 A Area of Triangles (pages ) You can divide a parallelogram into two congruent triangles by drawing a diagonal. Since the formula for the area of a parallelogram is A bh, then the formula for the area of a triangle is A 2 bh. Finding the The area A of a triangle equals half of the product of Area of a the length of the base b and the height h. Triangle A bh 2 h b A What is the area of a triangle with a height of 25 cm and a base of 36 cm? The area of a triangle is 54 in 2 and the height is 2 in. Find the base. A bh Write the formula. A 2 2 bh Write the formula. A (36)(25) Substitute the values you know (b)(2) Substitute the values you know. A 450 cm 2 Multiply to find the area. 54 6b Multiply. 9 in. b Find the area of a triangle that has a 2. A triangle has a base of 8 cm and an base of yd and height of yd. area of 64 cm 2. Find the height. 3 HINT: Use the formula and multiply. HINT: Substitute in the formula and solve for h. Find the area of each triangle m 4 cm 9 in. 20 m 2 in. 6. Flags The flag of the country of Guyana has a red triangle on it. If the base of the triangle is 30 inches and the height is 26 inches, what is the area of the triangle? Standardized Test Practice How long is the base of a triangle that has an area of 63 square centimeters and a height of 7 centimeters? A 7 cm 9 cm C 6 cm D 8 cm Answers:. yd cm 00 m 2 6 cm in in 2 6 D 99 Mathematics: Applications and Concepts, Course
3 A Area of Circles (pages ) If you cut a circle into a number of equal-sized pie-shaped pieces and arrange them carefully, you can form a rough parallelogram. The height of the parallelogram is about equal to the radius of the circle. The base is about equal to 2 of the circumference of the circle. This would mean that the area is about 2 Cr. Substitute the circumference formula for C and you get the following equation. Finding the The area A of a circle equals the product of and the square Area of a of the radius r. Circle A r 2 r A Find the area of a circle with a radius of Find the area of a circle that has a 7 cm. Use 4 for. diameter of 5 inches. Use 4 for. A r 2 Write the formula. A r 2 Write the formula. A 4(7) 2 Substitute the values you know. A 4(2.5) 2 r 2 d or 2.5 in. A 54 cm 2 Use a calculator and round. A 9.6 in 2 Use a calculator and round.. A circle has a radius of 2 in. What is 2. The diameter of a circle is 2 yd. Find its area? Use 4 for. its area. Use 4 for. HINT: Write the formula and substitute. HINT: First find the radius. Find the area of each circle to the nearest tenth. Use 4 for m 2 ft 3 in. 6. diameter, 8 centimeters radius, 5 meters radius, 0 inches 9. Standardized Test Practice What is the area of a circle that has a diameter of 30 centimeters? A ,826 cm 2 C 76.6 cm 2 D cm 2 Answers:. about 2.6 in 2 2. about 8 yd m 2 0 ft in m 2 30 in 2 9. D 00 Mathematics: Applications and Concepts, Course
4 A Three-Dimensional Figures (pages ) A three-dimensional figure encloses a part of space. The flat surfaces are called faces. The segments formed by the intersecting faces are the edges. The edges intersect at the vertices. prism: two parallel and congruent faces, called bases Identifying pyramid: triangular faces; one base Three- Prisms and pyramids are named by the polygon(s) at their base(s). Dimensional cone: curved surface; one circular base Figures cylinder: curved surface; two circular bases sphere: all the points are the same distance from the center A Identify this figure. The faces are rectangular, so the figure is a prism. The bases are rectangles, so it is a rectangular prism. Identify this figure. The surface is curved and there are two circular bases. The figure is a cylinder.. Is a square a two-dimensional or a 2. How many faces, edges, and vertices three-dimensional figure? are there in the figure of Example A? HINT: Does a square have the three dimensions of length, width, and height? HINT: Think of a closed box shape. Identify each figure How many edges does this rectangular prism have? Gift Wrapping Juanita bought her mother a candle in the shape of a square pyramid for her birthday. How many faces does the candle have for Juanita to cover with wrapping paper? Standardized Test Practice How many faces does a triangular pyramid have? A 4 3 C 5 D 2 Answers:. two-dimensional 2. 6; 2; 8 cube (or square prism) sphere 5. cone A 0 Mathematics: Applications and Concepts, Course
5 A Volume of Rectangular Prisms (pages ) The amount of space inside a three-dimensional figure is called its volume. Volume is expressed in cubic units. Finding the The volume V of a rectangular prism equals the Volume of a product of its length, its width w, and its height h. Rectangular Prism V wh, or V h, where is the area of the base. h w A Find the volume of a rectangular prism that is 8 by 9 by 7 inches. A cereal box is 29 cm tall and its top measures 7 cm by 20 cm. Find the volume. V wh Write the formula. V h Write the formula. V 8(9)(7) Substitute the values you know. V 20(7)(29) Substitute the values you know. V 504 in 3 Multiply to find the volume. V 4,060 cm 3 Multiply to find the volume.. What is the volume of a storage shed 2. A rectangular prism has a height of 7 feet high with a floor that is 0 feet 2 yards, a width of 0.6 yards, and a by 9 feet? length of.4 yards. Find the volume. HINT: Do you know the length, width, and height? HINT: Write the formula and substitute. Find the volume of each rectangular prism m 5 cm 3 m 20 cm 5 m 7 in. 5 in. 2 in. 6. What is the volume of a rectangular prism that is 2 mm high, 0 mm wide, and 8 mm long? Hobbies Mr. Maki is building a new flower bed. The bed is 3 feet wide, 0 feet long, and.5 feet deep. How many cubic feet of dirt will he need for his new flower bed? Standardized Test Practice Find the volume of a rectangular prism that is 5 feet wide, 8 feet tall, and feet long. A 55 ft ft 3 C 440 ft 3 D 40 ft 3 Answers:. 630 ft yd 3 30 m cm in ,60 mm 3 45 ft 3 C 02 Mathematics: Applications and Concepts, Course
6 A Surface Area of Rectangular Prisms (pages ) The surface area of a three-dimensional object is the total area of its faces and curved surfaces. Finding the Surface Area of a Rectangular Prism Find the area of the top and bottom bases. Find the area of the front and back faces. Find the area of the right and left sides. Add all these areas to find the total surface area of the prism. A Find the surface area of a box that is 8 ft by 6 ft by 3 ft. Area of the top is 8 Area of the front is 6 Area of the side is 3 6. There are 2 of each face. 8 ft Total area 2(24) 2(48) 2(8) or 80 ft 2 6 ft 3 ft What is the surface area of a rectangular prism with length 3 in., width 7 in., and height 2 in.? Area 2 (3 7) 2 (3 2) 2(7 2) Area 2(2 6 4) Area 2(4) Area 82 in 2. Find the surface area of a cube that 2. Find the surface area of a rectangular has an edge of 3 yards. prism that is. by 2.4 cm by 5.7 cm. HINT: A cube is a rectangular prism with HINT: egin by making a sketch and labeling it. 6 congruent faces. Find the surface area of each rectangular prism in. 3 in. 2 in. 6. length 2 ft length length 5 m width 3 ft width 9 cm width 7 m height 8 ft height cm height 8 m 9. Decorating Josie is putting wallpaper in her room. If her room is 0 feet wide, 2 feet long and 8 feet high, how much wallpaper will she need? Remember, she will not wallpaper the ceiling or the floor. 8 m 0 m 4 m ft 6 ft 5 ft 0. Standardized Test Practice What is the surface area of a 20-cm cube? A,200 cm 2 2,400 cm 2 C 400 cm 2 D 4,400 cm 2 Answers:. 54 yd cm 2 62 in m ft ft 2 78 cm m ft Mathematics: Applications and Concepts, Course
7 Chapter 4 Review Geometry Carnival. You want to make a target like the ones you saw at a carnival. You want the bull s-eye at the center to have less than 0 of the area of the whole target. Does a target with the measurements shown at the right meet this requirement? 9 cm ull s-eye 2. At the same carnival, you came across a very interesting game. Two tanks are partially filled with water as shown below. You must place solid prism C into one of the containers without spilling a drop of water to win a prize. Containers A and are open on the top. A C 8 cm 4 cm 4 cm 2 cm 5 cm 5 cm 5 cm 9 cm 2 cm 4 cm Into which container can you drop prism C without spilling water? Explain. Answers are located on p Mathematics: Applications and Concepts, Course
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