Calculating Surface Area of Composite Figures Made Easy

3/27/24, 1:59 PM Lesson Activity: Surface Area of Composite Figures https://f1.app.edmentum.com/courseware-delivery/ua/136621/45616316/aHR0cHM6Ly9mMS5hcHAuZWRtZW50dW0uY29tL2x0aS92Mi9sZWFybmV… 1/6 Lesson Activity Surface Area of Composite Figures This activity will help you meet this educational goal: You will apply formulas to find the surface area of a composite figure. Directions Read the instructions for this self-checked activity. Submit your response to each question and check your answers. At the end of the activity, write a brief evaluation of your work. Activity A family is repairing the roof and the outside of their old barn. Use the image to answer the questions in this activity. Question

3/27/24, 1:59 PM Lesson Activity: Surface Area of Composite Figures https://f1.app.edmentum.com/courseware-delivery/ua/136621/45616316/aHR0cHM6Ly9mMS5hcHAuZWRtZW50dW0uY29tL2x0aS92Mi9sZWFybmV… 2/6 Part A The barn represents a composite solid. What three-dimensional figures best model the barn? Select the correct answer. Correct! Explanation: The bottom portion of the barn can be modeled by a rectangular prism since all of its faces are rectangles. The top portion of the barn can be modeled by a triangular prism since the front and back sides of the roof are in the shape of a triangle. a triangular prism and a rectangular prism a triangular pyramid and a rectangular prism a triangular prism and a rectangular pyramid a triangular pyramid and a rectangular pyramid

3/27/24, 1:59 PM Lesson Activity: Surface Area of Composite Figures https://f1.app.edmentum.com/courseware-delivery/ua/136621/45616316/aHR0cHM6Ly9mMS5hcHAuZWRtZW50dW0uY29tL2x0aS92Mi9sZWFybmV… 3/6 Part B What is the area of the bottom portion of the barn that will need repairs? Type the correct answer in each box. Use numerals instead of words. The lateral area of the bottom portion is square feet. Correct! Explanation: The bottom portion that models the barn is a rectangular prism. The lateral area of a prism is Ph , where P is the perimeter of the base and h is the height of the prism. The base of the prism is where the barn is touching the ground and has dimensions of 50 feet by 40 feet. The perimeter of the base is 180 feet, and the height is 25 feet. So, the lateral area of the bottom portion is 4,500 square feet. Question 4500

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3/27/24, 1:59 PM Lesson Activity: Surface Area of Composite Figures https://f1.app.edmentum.com/courseware-delivery/ua/136621/45616316/aHR0cHM6Ly9mMS5hcHAuZWRtZW50dW0uY29tL2x0aS92Mi9sZWFybmV… 4/6 Part C What is the surface area of the top portion of the barn that will need repairs, including the roof? Explain how you determined your answer. Answer: So, the two rectangles representing the roof are congruent and have dimensions of 50 feet by 202 feet. Calculate their area. Space used (includes formatting): 142 / 15000 The top portion of the barn is modeled by a triangular prism, where the base of the prism is a triangle. The bottom face of the triangular prism with dimensions of 40 feet by 50 feet is not on the surface of the barn, so we don't need to find its area. Since we know the base and the height of the two triangles, calculate the area of the two base triangles. Find the unknown side lengths of the triangular base using special right triangles. The height with half the base creates a triangle, where the legs both measure 20 feet. So, the hypotenuse, which is also the other two side lengths of the base triangle, measure feet. So, the two rectangles representing the roof are congruent and have dimensions of 50 feet by feet. Calculate their area. Hide Sample Answer

3/27/24, 1:59 PM Lesson Activity: Surface Area of Composite Figures https://f1.app.edmentum.com/courseware-delivery/ua/136621/45616316/aHR0cHM6Ly9mMS5hcHAuZWRtZW50dW0uY29tL2x0aS92Mi9sZWFybmV… 5/6 Add these two areas together to find the surface area of the top portion of the barn. So, the surface area of the top portion of the barn is about 3,628 square feet. Part D Using your answers from parts B and C, what is the total surface area of the barn that will need repairs, including the roof? Answer: Space used (includes formatting): 346 / 15000 The total surface area of the barn that will need repairs is the lateral surface area of the rectangular prism at the bottom and the surface area of the triangular prism at the top, excluding the rectangular face with dimensions of 50 feet by 40 feet. Add the values from parts B and C together to find the total surface area. So, the total surface area of the barn that needs repairs is about 8,128 square feet. 8,128 square feet. Hide Sample Answer

3/27/24, 1:59 PM Lesson Activity: Surface Area of Composite Figures https://f1.app.edmentum.com/courseware-delivery/ua/136621/45616316/aHR0cHM6Ly9mMS5hcHAuZWRtZW50dW0uY29tL2x0aS92Mi9sZWFybmV… 6/6 Self-Evaluation How did you do? Rate your work on a scale of 1 to 5, with 5 as the highest score. Then write a brief evaluation of your work below. Note what you learned and what challenged you. Answer: 5, I did good and got all questions right. Space used (includes formatting): 49 / 15000

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Surface Area of Pyramids and Cones_ Tutorial

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