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Area & Perimeter

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**Objectives: Essential Question: Area & Perimeter**

Develop fluency in the use of formulas to solve problems. Essential Question: How can I use formulas to find the perimeter and area of simple geometric figures?

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**Vocabulary: Area & Perimeter**

Polygon: a closed plane figure bounded by three or more line segments. Quadrilateral: any four sided polygon. Parallelogram: a quadrilateral whose opposite sides are parallel. Square: a four sided polygon characterized by four right angles and four sides of equal length. Rectangle: a four sided polygon characterized by four right angles and opposite sides of equal measure. Triangle: a three sided polygon. Circle: a closed plane curve consisting of all points at a given distance from a point within it called the center.

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**Polygons: Area & Perimeter What do they look like…**

A regular polygon is a any polygon in which all sides and angles are congruent. An irregular polygon is a polygon whose sides are not all the same length and/or whose interior angles do not all have the same measure.

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**Polygons: Area & Perimeter**

The following are some examples of regular polygons:

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**Triangles: Area & Perimeter**

First lets focus on Triangles since they represent the smallest polygon: triangles

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**Triangles: Area & Perimeter A = ½bh height (h) height (h) base (b)**

The height is the shortest distance from a base to the opposite vertex height (h) height (h) base (b) base (b) The base of a triangle can be any one of its sides A = ½bh

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**A = ½bh A = ½(8)(5) A = 20 sq cm Example 1: Triangles Area & Perimeter**

Find the area of the triangle. A = ½bh A = ½(8)(5) A = 20 sq cm

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**A = ½bh A = ½(15)(3) A = 42.5 sq ft Example 2: Triangles**

Area & Perimeter Example 2: Triangles Find the area of the triangle. A = ½bh A = ½(15)(3) A = 42.5 sq ft

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**A = ½bh A = ½(15.5)(4.4) A = 31.4 sq mm Example 3: Triangles**

Area & Perimeter Example 3: Triangles Find the area of the triangle. A = ½bh A = ½(15.5)(4.4) A = 31.4 sq mm

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**Analyzing Quadrilaterals:**

Area & Perimeter Analyzing Quadrilaterals:

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**Quadrilaterals: Area & Perimeter**

Now lets focus on some important kinds of Quadrilaterals: Square Rectangle Parallelogram Trapezoid

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**Squares: Area & Perimeter A = lw = bh Side Parallel sides Side**

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**Example 4: Squares P = 4s P = 4 · 4 P = 16 sq in A = s2 A = 42**

Area & Perimeter Example 4: Squares Find the perimeter and area of the square. P = 4s P = 4 · 4 P = 16 sq in A = s2 A = 42 A = 16 sq in

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**Example 5: Squares P = 4s P = 4 · 7 P = 28 sq in A = s2 A = 72**

Area & Perimeter Example 5: Squares Find the perimeter and area of a square whose sides measure 7 inches. P = 4s P = 4 · 7 P = 28 sq in A = s2 A = 72 A = 49 sq in

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**Rectangles: Area & Perimeter A = lw = bh Width = Height Parallel sides**

Length = Base Parallel sides A = lw = bh

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**Example 6: Rectangles P = 2l + 2w P = 2(9) + 2(4) P = 22 in A = lw**

Area & Perimeter Example 6: Rectangles Find the perimeter and area of the rectangle. P = 2l + 2w P = 2(9) + 2(4) P = 22 in A = lw A = (9)(4) A = 36 sq in

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**Example 7: Rectangles P = 2l + 2w P = 2(7) + 2(4) P = 22 sq cm A = lw**

Area & Perimeter Example 7: Rectangles Find the perimeter and area of a rectangle whose length and width measure 7cm and 4cm. P = 2l + 2w P = 2(7) + 2(4) P = 22 sq cm A = lw A = (7)(4) A = 28 sq cm

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**Parallelograms: Area & Perimeter Original figure**

Draw a vertical line from top left vertex to the base of the figure Remove the piece to the left of the vertical line and translate it to the other side of the figure The new figure is a rectangle or square

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**Parallelograms: Area & Perimeter A = bh height**

The shortest distance from the base to the opposite side is the height of the parallelogram base The base of a parallelogram can be any one of its sides A = bh

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**Example 8: Parallelograms**

Area & Perimeter Example 8: Parallelograms Find the area of the parallelogram. The base is 6 and the height is 4. A = b · h A = 6 · 4 A = 24 sq un

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**Example 9: Parallelograms**

Area & Perimeter Example 9: Parallelograms Find the area of the parallelogram. The base is 9 and the height is 6. A = b · h A = 6 · 4 A = 24 sq un 6 9

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**Example 10: Parallelograms**

Area & Perimeter Example 10: Parallelograms Find the area of each parallelogram. 1 A = b · h A = (4)(4) A = 16 sq units 2 A = b · h A = (4)(3) A = 12 sq units A = b · h A = (7)(3) A = 21 sq units 3

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**Trapezoids: Area & Perimeter A = ½h(b1 + b2) Parallel sides base 1**

height Parallel sides base 2 A = ½h(b1 + b2)

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**Example 11: Trapezoids A = ½h(b1 + b2) A = ½(15)(16 + 21)**

Area & Perimeter Example 11: Trapezoids Find the area of the trapezoid. A = ½h(b1 + b2) A = ½(15)( ) A = (7.5)(37) A = sq cm

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**Example 12: Trapezoids A = ½h(b1 + b2) A = ½(26.6)(19.2+30.4)**

Area & Perimeter Example 12: Trapezoids Find the area of the trapezoid. A = ½h(b1 + b2) A = ½(26.6)( ) A = (13.3)(49.6) A = sq m

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**A = ½h(b1 + b2) A = ½(21)(8.1+28.2) A = (10.5)(36.3) A = 381.15 sq m**

Area & Perimeter Example 13: Trapezoids Find the area of the trapezoid. A = ½h(b1 + b2) A = ½(21)( ) A = (10.5)(36.3) A = sq m

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**Independent Practice: Triangles**

Area & Perimeter Independent Practice: Triangles Find the area of each triangle.

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**Independent Practice: Triangles**

Area & Perimeter Independent Practice: Triangles Answers. 1. A = 18 sq in A = sq m 3. A = 185 sq m A = sq cm

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**Independent Practice: Parallelograms**

Area & Perimeter Independent Practice: Parallelograms Answers. 4.2 4 12 5.7 9 9.7 2.3 3.1

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**Independent Practice: Parallelograms**

Area & Perimeter Independent Practice: Parallelograms Find the area of each parallelogram. 4.2 4 12 5.7 A = 48 sq un A = sq un 9 9.7 A = 20.7 sq un A = sq un 2.3 3.1

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**Independent Practice: Trapezoids**

Area & Perimeter Independent Practice: Trapezoids Find the area of each trapezoid. 3. b1 = 8½ m, b2 = 3¼ m, h = 7¾ m 4. b1 = 16cm, b2 = 9cm, h = 12cm

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**Independent Practice: Trapezoids**

Area & Perimeter Independent Practice: Trapezoids Answers. 1. A = /189 sq in A = sq ft 3. A = sq m 4. A = 150 sq cm

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**Summary: A = lw = bh A = lw = bh A = ½bh A = bh Area & Perimeter**

Formula Review: A = lw = bh A = lw = bh A = ½bh A = ½h(b1 + b2) A = bh

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Area & Perimeter HOMEWORK

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**Area & Circumference of Circles**

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**Objectives: Essential Question: Area & Perimeter**

Develop fluency in the use of formulas to solve problems. Essential Question: How can I use formulas to find the perimeter and area of simple geometric figures?

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**Circles: Area & Perimeter What do they look like…**

A circle is a geometric shape with all points the same distance from the center. - The circle above is called circle A since the center is at point A. (circles are always named by their centers)

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Area & Perimeter HOMEWORK

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