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Comparing Shapes' Perimeters and Areas

This test item asks students to compare the perimeters or circumferences of different shapes and determine which one would use the most or all of the given tape. The shapes included are a square, circle, right triangle, and rectangle.

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Comparing Shapes' Perimeters and Areas

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  1. Largest Area Terri has 19 feet of tape to mark an area in the classroom where the students may read. Which of these shapes has a perimeter or circumference that would use most or all of the tape? A square with side length of 5 feet B circle with the radius of 3 feet C right triangle with each leg length of 6 feet D rectangle with a length of 8 feet and a width of 3 feet Read the Test Item You are asked to compare the perimeters orcircumference of four different shapes. Example 3

  2. Largest Area Solve the Test Item Find each perimeter or circumference. Square P = 4s Perimeter of a square = 4(5) s = 5 = 20 feet Simplify. Circle C = 2r Circumference = 2(3) r = 3 = 6 Simplify. ≈ 18.85 feet Use a calculator. Example 3

  3. . Largest Area Right Triangle Use the Pythagorean Theorem to find the length of the hypotenuse. c2 = a2+b2 Pythagorean Theorem = 62+62a = 6, b = 6 = 72 Simplify. ≈ 8.49 Use a calculator. P = a + b + c Perimeter of a triangle  6 + 6 + 8.49 Substitution  20.49 feet Simplify. Example 3

  4. Largest Area Rectangle P = 2ℓ+2w Perimeter of a rectangle = 2(8)+2(3)ℓ = 8, w = 3 = 22 feet Simplify. The only shape for which Terri has enough tape is the circle. Answer: The correct answer is B. Example 3

  5. Content Standards G.GPE.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. Mathematical Practices 2 Reason abstractly and quantitatively. 6 Attend to precision. CCSS

  6. Concept

  7. Each of the following shapes has a perimeter of about 88 inches. Which one has the greatest area? • a rectangle with a length of 26 inches • B. a square • a right triangle with each leg length of 26 inches • D. a circle with radius of 14 inches Example 3

  8. Perimeter and Area on the Coordinate Plane Find the perimeter and area of a pentagon ABCDE with A(0, 4), B(4, 0), C(3, –4), D(–3, –4), and E(–3, 1). Example 4

  9. Find the perimeter of quadrilateral WXYZ with W(2, 4), X(–3, 3), Y(–1, 0), and Z(3, –1). A. 17.9 B. 22 C. 13.3 D. 9.1 Example 4

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