lesson 7 homework practice surface area of pyramids answer key

Surface Area - Pyramids

Examples, videos, and solutions to help Grade 7 students learn how to find the surface area of three-dimensional objects whose surface area is composed of triangles and quadrilaterals, specifically focusing on pyramids.

New York State Common Core Math Grade 7, Module 3, Lesson 22

Lesson 22 student outcomes.

• Students find the surface area of three-dimensional objects whose surface area is composed of triangles and quadrilaterals, specifically focusing on pyramids. They use polyhedron nets to understand that surface area is simply the sum of the area of the lateral faces and the area of the base(s).

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Lesson Surface area of pyramids

Chapter 7, Lesson 8: Surface Area of Pyramids

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Explanation:

A paper model of the Khafre pyramid in Egypt has a square base 7.2 centimeters on each side. The slant height is 6 centimeters How much paper was used to make the model?

Be Precise A triangular pyramid has a surface area of 336 square inches. It is made up of equilateral triangles with side lengths of 12 inches. What is the slant  height?

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Surface Area of Prisms and Pyramids Worksheet with Answer Key

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FABULOUS Surface-Area-of-Prisms-and-Pyramids Geometry Practice-Worksheet, you'll love using this year after year! Answer Key included! Great for Math Stations or Centers, Home School, Distance Learning, Homework or Guided Practice!

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Chapter 7, Lesson 8: Surface Area of Pyramids

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Into Math Grade 6 Module 13 Lesson 1 Answer Key Explore Nets and Surface Area

We included  HMH Into Math Grade 6 Answer Key PDF   Module 13 Lesson 1 Explore Nets and Surface Area to make students experts in learning maths.

HMH Into Math Grade 6 Module 13 Lesson 1 Answer Key Explore Nets and Surface Area

I Can make and use nets to find the surface areas of rectangular and triangular prisms and pyramids.

Spark Your Learning

Turn and Talk If Caleb decides not to paint the bottom of the storage box, will he have enough paint to paint the storage box? Explain. Answer: Yes, then he should have enough paint. This means one side he should not paint then we can calculate like this: 3.75 + 8 = 11.75 What we did is avoided the bottom part in the calculation. For the top part: 2.5 x 1.5 = 3.75 For the remaining parts = 2(L × H + W × H) = 2(4) = 8 We added both values then we get 11.75 sq.ft

Build Understanding

Question 1. A solid figure is a three-dimensional figure because it has three dimensions: length, width, and height. Connect to Vocabulary A net is an arrangement of two-dimensional figures that can be folded into a closed solid figure.

C. Trace both nets in Part B on a separate sheet of paper. Cut out each net. Then fold the nets. Which net will fold into a closed three¬dimensional figure? What is the three-dimensional figure? Answer: When we fold the purple figure it is easily shown that it is a cube. And when we fold a green net it is overlapping. Therefore, purple forms a cube.

D. Write an equation to represent the area of one face of the cube. Answer: side x side = side^2 Explanation: The definition of the surface area of a given cube states that the total surface area is equal to the sum of all the areas of the faces of the cube. Since the cube has six faces, therefore, the total surface area of the cube will be equal to the sum of all six faces of the cube. Since the surface of the cube is in a square shape. Hence, the area of each face of the cube is equal to the square of the edge. Let the length of an edge of a cube is a. Therefore, the area of one face = a 2     [By area of square formula]

E. If the edge of the cube measures 4 centimetres, what is the area of one face of the cube? Answer: According to the above information: Let the length of an edge of a cube is a. Therefore, the area of one face = a 2     [By area of square formula] a = 4 4 x 4 = 16 square.cms

F. What is the total area of all 6 faces of the cube? Answer: There are total 6 faces. Therefore, TSA of cube = a 2  + a 2  + a 2  + a 2  + a 2  +a 2 TSA of cube = 6a 2 A cube consists of an ‘n’ number of square units. Hence the space covered by these square units on the surface of the cube is the surface area. Basically, the surface area is the sum of all the areas of all the shapes that cover the surface of the shape or object. In the case of a cube, there are 6 faces. So the surface area will be the sum of all the area of six faces. We know that one face of the cube is 16 square.cms According to the formula: The total area of all 6 faces of the cube = 16(6) = 96 square cms

Turn and Talk What do all six faces of the cube have in common? Is there another way to calculate the total area of the faces? Answer: All six faces of the cube have the same shape and the same area. Another way to calculate the total area of the faces is to add the 16 for 6 times. 16 + 16 + 16 + 16 + 16 + 16

Connect to Vocabulary Surface area is the sum of the areas of the faces, or surfaces, of a three-dimensional figure. A pyramid is a three-dimensional figure with a polygon base and triangular sides that all meet at a common vertex.

B. What formula can you use to find the area of one triangular face? Answer: The formula we can use is: Area = bh/2 area = 7(5)/2 area = 35/2

C. What is the area of one triangular face? Answer: According to the above formula, we can find out the area of one triangular face. Area = bh/2 area = 7(5)/2 area = 35/2 area = 17.5 square inches.

D. What is the area of the square base? Answer: The base of a square pyramid is square-shaped. Thus, the base area of the square pyramid can be calculated using the formula, Base Area of Pyramid = a^2, where, a is the length of the base of square pyramid. we know that the square base is 5. area = 5 . 5 area =25 square inches.

E. How can you find the surface area of the square pyramid? Answer: Surface Area of a square pyramid = Area of the base + Area of 4 triangles Then, the formula to calculate the surface area is: Surface Area = s 2  + 2sl square units. According to the above information (part D and part C). We substituted the values in the formula. Surface area = 25 + (17.5)4 Surface area = 25 + 75 Syrface area = 95 square inches.

F. What is the surface area of the square pyramid? Answer: According to the above information (part E) Therefore, the answer for the surface area of the square pyramid is 95 square inches.

Turn and Talk Is there another way to solve for the surface area? Explain. Answer: – To find the surface area, work out the area of each face and add them together. – Well you can also multiply the perimeter by the length of the edge, then divide by the length of the face.

Check Understanding

On Your Own

B. How much cardboard do they need for each container? Answer: The surface area of a triangular pyramid = bh/2 There should be 4 triangles so the formula is: surface area = 4(bh/2) surface area = 4(10 x 8.7)/2 surface area = 4(87)/2 surface area = 348/2 surface area = 174 square cms.

For Problems 4-7, identify what solid figure the net folds into. Then find the surface area of the net.

I’m in a Learning Mindset!

How did I apply prior knowledge to find the surface area of a square pyramid in Task 2? Answer:

Lesson 13.1 More Practice/Homework

For Problems 3-4, identify what solid figure the net folds into. Then find the surface area of the figure.

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