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20S Applied Math Mr. Knight – Killarney School Slide 1 Unit: Real Number System Lesson: 2D3D-L1 Perimeter and Area of 2D Shapes Perimeter and Area of 2D Shapes Learning Outcome B-4 2D3D-L1 Objectives: To perform routine applied mathematics operations correctly on a scientific calculator.

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20S Applied Math Mr. Knight – Killarney School Slide 2 Unit: Real Number System Lesson: 2D3D-L1 Perimeter and Area of 2D Shapes Perimeter is the total length around the outside of a closed geometric figure. To find the perimeter of a polygon, such as a rectangle, you add the lengths of all sides of the figure. If the figure is circular, you find its circumference. Theory – Perimeter

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20S Applied Math Mr. Knight – Killarney School Slide 3 Unit: Real Number System Lesson: 2D3D-L1 Perimeter and Area of 2D Shapes Theory – Perimeter of a Triangle The following formulas can be used to calculate the perimeter of geometric figures. You do not have to memorize the formulas for these specific cases. The perimeter of a triangle is simply the sum of the length of the three sides. Triangles a)Scalene: P = a + b + c (no sides the same length) (b) Isosceles: P = 2a + b (two sides the same length) c) Equilateral: P = 3a (all sides the same length)

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20S Applied Math Mr. Knight – Killarney School Slide 4 Unit: Real Number System Lesson: 2D3D-L1 Perimeter and Area of 2D Shapes Theory – Perimeter of a Quadrilateral The perimeter of four-sided figures (quadrilaterals) can be calculated by finding the sum of the four sides. In some special cases the sides have the same length and an abbreviated formula is possible though not necessary. (a) General: P = a + b + c + d (b) Trapezoid: P = a + b + c + d (c) Parallelogram: P = 2a + 2b (d) Rectangle: P = 2l + 2w (e) Square: P = 4s (f) Rhombus: P = 4a

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20S Applied Math Mr. Knight – Killarney School Slide 5 Unit: Real Number System Lesson: 2D3D-L1 Perimeter and Area of 2D Shapes Theory – Perimeter of a Quadrilateral The perimeters of pentagons, hexagons, and other polygons are calculated in the same way – add together the lengths of all sides of the figure. The perimeter of a circle is called its circumference. The circumference is found by using a formula: C = 2πr or C = πd, where r is the radius and d is the diameter. These formulae are essentially the same as 2r = d.

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20S Applied Math Mr. Knight – Killarney School Slide 6 Unit: Real Number System Lesson: 2D3D-L1 Perimeter and Area of 2D Shapes Example 1 (a) Find the perimeter of Δ ACB. (b) Find the perimeter of Δ ADB. (c) Find the perimeter of quadrilateral ACBD.

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20S Applied Math Mr. Knight – Killarney School Slide 7 Unit: Real Number System Lesson: 2D3D-L1 Perimeter and Area of 2D Shapes Example 2 (a) Find the perimeter of the square ABCD. (b) Find the circumference of the circle with centre E.

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20S Applied Math Mr. Knight – Killarney School Slide 8 Unit: Real Number System Lesson: 2D3D-L1 Perimeter and Area of 2D Shapes Theory - Area The area of a geometric figure is the amount of space that the 2D figure covers. For example, you can find the area of the rectangle below by counting the squares that are contained in the figure. The rectangle covers eight squares or has an area of eight square units. The algebraic model or formula that you can apply to calculate this area is as follows: A = l x w = 4 units x 2 units = 8 sq. units

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20S Applied Math Mr. Knight – Killarney School Slide 9 Unit: Real Number System Lesson: 2D3D-L1 Perimeter and Area of 2D Shapes Theory – Area of Geometric Shapes The formulas for finding the areas of other geometric figures are: Anytime height (h) is used in a formula it must be measured perpendicular to the base. 1. Triangles: A = ½bh 2. Trapezoid: A = ½(a + b)h, where a and b must be the parallel sides 3. Parallelogram: A = bh 4. Rectangle: A = lw 5. Square: A = s 2 6. Rhombus: A = ah 7. Circle: A = πr 2

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20S Applied Math Mr. Knight – Killarney School Slide 10 Unit: Real Number System Lesson: 2D3D-L1 Perimeter and Area of 2D Shapes Theory – Area of Irregularly Shaped 2D Objects To find the areas of other more irregular shapes, break the figure into one or more of the above shapes and add the resulting areas. Example: To find the area of the above figure, draw in the line segment AC. Find the areas of the triangles ABC and ADC, and add the two areas.

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20S Applied Math Mr. Knight – Killarney School Slide 11 Unit: Real Number System Lesson: 2D3D-L1 Perimeter and Area of 2D Shapes Example 3 Find the area of the triangle ABC

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20S Applied Math Mr. Knight – Killarney School Slide 12 Unit: Real Number System Lesson: 2D3D-L1 Perimeter and Area of 2D Shapes Example 4 Find the area of the shaded region.

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20S Applied Math Mr. Knight – Killarney School Slide 13 Unit: Real Number System Lesson: 2D3D-L1 Perimeter and Area of 2D Shapes Example 5 Find the area of the figure. (All angles are 90 0 )

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20S Applied Math Mr. Knight – Killarney School Slide 14 Unit: Real Number System Lesson: 2D3D-L1 Perimeter and Area of 2D Shapes Example 6 Find the area of a uniform 1.2 m wide sidewalk around a flower garden as shown in the figure. (The sidewalk is shaded.)

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