## Exploring Area and Surface Area

### Mathematics, Grade 7

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#### Study Guide Exploring Area and Surface Area Mathematics, Grade 7

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EXPLORING AREA AND SURFACE AREA Area is the amount of surface a shape covers. Area is measured in square units, whether the units are inches, feet, meters or centimeters. The area formula for a triangle is: A = 1/2 · b · h, where b is the base and h is the height. The area formula for a circle is: A = π · r², where π is usually 3.14 and r is the radius of the circle. The area formula for a parallelogram is: A = b · h, where b is the base and h is the height. The area of a trapezoid is: A = (1/2)(b1 + b2) · h, where b1 is one base and b2 is the other base and h is the height. Surface area is the sum of all the areas of the surfaces of an object. The surface area of a rectangular prism is: SA = 2wl + 2lh + 2 hw. The surface area of a triangular prism is: SA = wl + lh + hw + bh. The surface area of a cylinder is: SA = r · h + r². The surface area of a sphere is: SA = r². For the surface area of a cylinder and a sphere, π is usually 3.14. A net of a figure is simply a flat pattern of the figure that when folded would form a solid figure. When comparing two similar figures, their surface areas should be in proportion to each other. © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.
How to use exploring area and surface area The area of any figure can be found if given the appropriate dimensions. For example, to find the area of a triangle, use the formula A = 1/2 · b · h , and fill in the base and the height. Then multiply the base and height together and divide by two to find the area. If the area of a triangle and one side of the triangle is given, the missing side can be found by using the same formula. This time the area will be filled in as well as either the base or the height, depending on what is given. By performing the operations, the result will be the missing side. Finding a missing side or diameter can be done with any shape and the area formulas for that shape. For example, what is the radius of a circle with an area of 78.5 units²? Ex. Area = 78.5 units² A = π · 78.5 = 3.14 · r ² 3.14 3.14 25 = 5 = r © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.
The surface area of any figure can be found using the appropriate formulas. For example, what is the surface area of a sphere with a radius of 5 inches? Ex. SA sphere = = (4)(3.14)(5²) = (4)(3.14)(25) = 314 inches² If the surface area and all other dimensions are given except one dimension, the missing dimension can be found by plugging in the surface area and given dimensions and solving for the missing dimension. Try This! 1. What is the area of a rectangle with a base of 3 m and a height of 5 m? 2. What is the area of the triangle with a base of 4 cm and a height of 12 cm? 3. What is the area of the circle with a diameter of 14 inches? 4. What is the area of a trapezoid with bases, 2 ft and 4 ft, and a height of 5 ft? © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.
5. What is the missing side of a rectangle with an area of 64 and a base of 4m? 6. What is the base of a triangle with an area of 39 and a height of 13 m? 7. What is the radius of a circle with an area of 28.26 cm²? 8. What is the surface area of a rectangle with a length of 2 cm, a width of 3 cm and a height of 5 cm? 9. What is the surface area of a cylinder with a radius of 12 in. and a height of 24 in.? 10. What is the surface area of a sphere with a diameter of 10 ft? © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.