Area of a a parallelogram
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Area of a a parallelogram
In a parallelogram, the height is a segment perpendicular to both bases
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• If a diagonal is drawn in a parallelogram, 2 identical triangles are formed.
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• The area of a parallelogram is twice the area of one of the triangles, so an expression to find the area of a parallelogram could be written
• A = 2 (1/2 bh) which simplifies to
• A = bh
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Area of a parallelogram
•A = bh• Where b is the length of the
base and h is the perpendicular height
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• Since rectangles, rhombuses, and squares are all parallelograms, the area of these shapes can also be found using the same formula
•A = bh
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Find the area of each of the following:
• Square rectangle
3 yd.
3 yd. 22 in.
12 in.
parallelogram15 ft
9 ft.8 ft.
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Trapezoid
• A trapezoid is a quadrilateral with exactly 1 pair of parallel sides
• The height of the trapezoid is the a segment that is perpendicular to both parallel sides of the trapezoid- these parallel sides are the bases- b1 and b2
b1
b2
h
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Area of a trapezoid
•A = 1/2 (b1 + b2 ) h
• Where b1 and b2 are the bases and h is the perpendicular height
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Finding areas of trapezoids
20 in
28 in.
6 in.
17 in.
24 in.
12 in.
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Rhombus
• A rhombus's diagonals are perpendicular and bisect each other
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Area of a rhombus
• Since a rhombus is a parallelogram, you can use the formula for parallelogram
• A = bh
• Or• You can use the diagonals formula
• A = 1/2 d1 d2
• Where d1 and d2 represent the diagonals of the rhombus
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Find the area of the rhombus
• Use the parallelogram formula or the diagonal formula
5 ft
6 ft30 in
11 in.