Perimeter and area
Mathematics, Grade 8
Perimeter and area
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Perimeter and area
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Perimeter and area
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Perimeter and area
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Perimeter and area
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Study Guide Perimeter and area Mathematics, Grade 8
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PERIMETER AND AREA What Is Perimeter and Area? • Perimeter is the measurement of the distance around a figure. It is measured in units and can be measured by inches, feet, blocks, meters, centimeters or millimeters. To find the perimeter of any figure, simply add up the measures of the sides of the figure. • Area is the amount of surface a shape covers. Area is measured in square units, whether the units are inches, feet, meters or centimeters. o The area formula for a parallelogram is: A = b · h , where b is the base and h is the height. o The area formula for a triangle is: A = 1/2 · b · h , where b is the base and h is the height. o 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. • The Pythagorean Theorem is a theorem that states the sum of the squares of the legs of a right triangle equals the square of the length of the hypotenuse. In mathematical terms, this is represented by a² + b² = c², where a and b are the length of the legs and c is the length of the hypotenuse of a right triangle. • The circumference is the distance around the circle, it is measured in terms of the diameter, and the formula is C = π · d, where π is 3.14 and d is the diameter. • The area of a circle is the amount of space it covers. The formula for the area of a circle is: A = π · r², where π is usually 3.14 and r is the radius of the circle. © 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 perimeter and area • Perimeter is the measurement of the distance around a figure. To get the perimeter of a rectangle with a length of 4 and a width of 5, add the length and the width and multiply times 2, to take into account all sides. If a figure is shown, the sides can just simply be added together. Perimeter can be found for any figure, whether it is a rectangle, parallelogram, triangle or trapezoid. • The circumference is the distance around the circle. If the diameter of the circle is known, the circumference can also be found using the formula C = π · d. If the radius is given, the diameter can be found by doubling the radius and then the circumference formula can be used. For example, what it the circumference of a circle with a radius of 6 cm? Ex. C = π · d C = (3.14)(2)(6) = 37.68 cm • 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. The area of rectangles, parallelograms, trapezoids and circles can also be found by using the appropriate formula. • The Pythagorean Theorem can only be used if a triangle is a right triangle. This would have to be stated in order to use the Pythagorean theorem. If a triangle is a right triangle and the sides are given, the hypotenuse can be found as follows: Ex. A right triangle has sides of 6 cm and 8 cm. a² + b² = c² 6² + 8² = c² 36 + 64 = c² 100 = c² √100 = c²; c =10 The hypotenuse of the triangle is 10 cm. The Pythagorean theorem can also be used if one leg and the hypotenuse are given to find the missing leg. The Pythagorean theorem is also used to prove that triangles are right triangles. © 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.
Try This! 1. What is the perimeter of a triangle with sides of 5 cm, 6 cm and 9 cm? 2. What is the circumference if C = π · d and π = 3.14? d = 12 d = 3 r = 7.5 3. What is the area of a rectangle with a base of 3 m and a height of 5 m? 4. What is the area of a trapezoid with bases of 4 cm and 9 cm and a height of 12 cm? 5. What is the area of the circle with a diameter of 14 inches? 6. A triangle is a right triangle. The legs are 8 cm and 14 cm. What is the length of the hypotenuse? 7. A right triangle has a hypotenuse of 26 ft and a leg that is 24 ft. What is the length of the missing leg? 8. A triangle has sides of 5 cm and 8 cm. The hypotenuse is 13. Is the triangle a right triangle? © 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.
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