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**Perimeter and Area of 2D Shapes**

2D3D-L1 Objectives: To perform routine applied mathematics operations correctly on a scientific calculator. Learning Outcome B-4

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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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**Scalene: P = a + b + c (no sides the same length)**

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 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) Theory – Perimeter of a Triangle

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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. General: P = a + b + c + d Trapezoid: P = a + b + c + d Parallelogram: P = 2a + 2b Rectangle: P = 2l + 2w (e) Square: P = 4s (f) Rhombus: P = 4a Theory – Perimeter of a Quadrilateral

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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. Theory – Perimeter of a Quadrilateral

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**(a) Find the perimeter of Δ ACB. (b) Find the perimeter of Δ ADB. **

Example 1 (a) Find the perimeter of Δ ACB. (b) Find the perimeter of Δ ADB. (c) Find the perimeter of quadrilateral ACBD. Example 1

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**(a) Find the perimeter of the square ABCD. **

Example 2 (a) Find the perimeter of the square ABCD. (b) Find the circumference of the circle with centre E. Example 2

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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 Theory - Area

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**2. Trapezoid: A = ½(a + b)h, where a and b must be the parallel sides **

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 = s2 6. Rhombus: A = ah 7. Circle: A = πr2 Theory – Area of Geometric Shapes

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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. Theory – Area of Irregularly Shaped 2D Objects

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**Find the area of the triangle ABC**

Example 3 Find the area of the triangle ABC Example 3

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**Find the area of the shaded region.**

Example 4 Find the area of the shaded region. Example 4

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**Find the area of the figure. (All angles are 900)**

Example 5 Find the area of the figure. (All angles are 900) Example 5

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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.) Example 6

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