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Surface Area




 


Video solutions to help Grade 7 students learn how to determine the surface area of three-dimensional figures, including both composite figures and those missing sections.

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Common Core For Grade 7

New York State Common Core Math Grade 7, Module 6, Lesson 24


Lessons 24 Student Outcomes


• Students learn how to determine the surface area of three-dimensional figures, including both composite figures and those missing sections.

Lessons 24 Summary


• To determine the surface area of a right prism, find the area of each lateral face and the two base faces, then add the areas of all the faces together.

Lesson 24

Opening Exercise

Example 1
Determine the surface area of the image.

Example 2
a. Determine the surface area of the cube.
b. A square hole with a side length of inches is drilled through the cube. Determine the new surface area.

Example 3
A right rectangular pyramid has a square base with a side length of 10 inches. The surface area of the pyramid is 260 in2 Find the height of the four lateral triangular faces.

Exercises 1–8
Determine the surface area of each figure. Assume all faces are rectangles unless it is indicated otherwise.

2. In addition to your calculation, explain how the surface area was determined.

4. In addition to your calculation, explain how the surface area was determined.

5. A hexagonal prism has the following base and has a height of 8 units. Determine the surface area of the prism.

6. Determine the surface area of each figure.
b. A cube with a square hole with 3 m side lengths has been drilled through the cube.
c. A second square hole with m side lengths has been drilled through the cube.

7. The figure below shows 28 cubes with an edge length of 1 unit. Determine the surface area.

8. The base rectangle of a right rectangular prism is 4 ft. × 6 ft. The surface area is 288 ft2. Find the height. Let h be the height in feet.





Lesson 24

Example 3
A right rectangular pyramid has a square base with a side length of 10 inches. The surface area of the pyramid is 260 in2Find the height of the four lateral triangular faces.
Lesson 24 Exit Ticket

Determine the surface area of the right rectangular prism after the two square holes have been drilled. Explain how you determined the surface area.



 


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