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Math Perimeter and Area Calculations in Different Figures

Learn how to find the perimeter and area of various figures, including triangles, trapezoids, parallelograms, and rhombi. Practice solving different math problems and improve your geometry skills.

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Math Perimeter and Area Calculations in Different Figures

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  1. A B C D Find the perimeter of the figure. Round to the nearest tenth if necessary. 48 cm 5-Minute Check 1

  2. A B C D Find the perimeter of the figure. Round to the nearest tenth if necessary. 37.9 ft 5-Minute Check 2

  3. A B C D Find the area of the figure. Round to the nearest tenth if necessary. 171.5 in2 5-Minute Check 3

  4. A B C D Find the area of the figure. Round to the nearest tenth if necessary. 3.4 m2 5-Minute Check 4

  5. A B C D Find the height and base of the parallelogram if the area is 168 square units. 12 units; 14 units 5-Minute Check 5

  6. A B C D The area of an obtuse triangle is 52.92 square centimeters. The base of the triangle is 12.6 centimeters. What is the height of the triangle? 8.4 centimeters 5-Minute Check 6

  7. Find areas of trapezoids. • Find areas of rhombi and kites. Then/Now

  8. Concept 1

  9. Area of a Trapezoid SHAVINGFind the area of steel used to make the side of the razor blade shown below. Area of a trapezoid h = 1, b1 = 3, b2 = 2.5 Simplify. Answer:A = 2.75 cm2 Example 1

  10. A B C D Find the area of the side of the pool outlined below. 302.5 ft2 Example 1

  11. OPEN ENDEDMiguel designed a deck shaped like the trapezoid shown below. Find the area of the deck. Read the Test Item You are given a trapezoid with one base measuring 4 feet, a height of 9 feet, and a third side measuring 5 feet. To find the area of the trapezoid, first find the measure of the other base. Example 2

  12. Solve the Test Item Draw a segment to form a right triangle and a rectangle. The triangle has a hypotenuse of 5 feet and legs of ℓ and 4 feet. The rectangle has a length of 4 feet and a width of x feet. Example 2

  13. Use the Pythagorean Theorem to find ℓ. a2 + b2 = c2 Pythagorean Theorem 42 + ℓ2 = 52 Substitution 16 + ℓ2 = 25 Simplify. ℓ2 = 9 Subtract 16 from each side. ℓ = 3 Take the positive square root of each side. Example 2

  14. By Segment Addition, ℓ + x = 9. So, 3 + x = 9 and x = 6. The width of the rectangle is also the measure of the second base of the trapezoid. Area of a trapezoid Substitution Simplify. Answer: So, the area of the deck is 30 square feet. Example 2

  15. The area of the trapezoid is the sum of the areas of the areas of the right triangle and rectangle. The area of the triangle is or 6 square feet. The area of the rectangle is (4)(6) or 24 square feet. So the area of the trapezoid is 6 + 24 or 30 square feet. Check Example 2

  16. A B C D Ramon is carpeting a room shaped like the trapezoid shown below. Find the area of the carpet needed. 88 ft2 Example 2

  17. Concept 2

  18. Area of a Rhombus and a Kite A. Find the area of the kite. Area of a kite d1 = 7 and d2 = 12 Answer: 42 ft2 Example 3A

  19. Area of a Rhombus and a Kite B. Find the area of the rhombus. Step 1 Find the length of each diagonal. Since the diagonals of a rhombus bisect each other, then the lengths of the diagonals are 7 + 7 or 14 in. and 9 + 9 or 18 in. Example 3B

  20. Simplify. 2 Area of a Rhombus and a Kite Step 2 Find the area of the rhombus. Area of a rhombus d1 = 14 and d2 = 18 Answer: 126 in2 Example 3B

  21. A B C D A. Find the area of the kite. 58.5 ft2 Example 3A

  22. A B C D B. Find the area of the rhombus. 180 in2 Example 3B

  23. 1 __ 2 Step 1 Write an expression to represent each measure. Let x represent the length of one diagonal. Then the length of the other diagonal is x. Use Area to Find Missing Measures ALGEBRA One diagonal of a rhombus is half as long as the other diagonal. If the area of the rhombus is 64 square inches, what are the lengths of the diagonals? Example 4

  24. Does the Rhombus Formula work for a Square? • s = 4 • d = ?

  25. A = 64, d1= x, d2 = x 1 __ 2 Use Area to Find Missing Measures Step 2 Use the formula for the area of a rhombus to find x. Area of a rhombus Simplify. 256 = x2 Multiply each side by 4. 16 = x Take the positive square root of each side. Example 4

  26. Answer: So, the lengths of the diagonals are 16 inches and (16) or 8 inches. 1 __ 2 Use Area to Find Missing Measures Example 4

  27. A B C D Trapezoid QRST has an area of 210 square yards. Find the height of QRST. 6 yd Example 4

  28. Concept 3

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