Triangles, Quadrilaterals, Nets, Prisms & Composite Polygons.
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Transcript of Triangles, Quadrilaterals, Nets, Prisms & Composite Polygons.
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Finding Area & Volume
Triangles, Quadrilaterals, Nets, Prisms & Composite Polygons
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Formulas You Need To Know
PARALLELOGRAM
A = b x h 2
A = b x h
TRIANGLE
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TRAPEZOID
1) add the top & bottom bases
2) multiply the sum by height 3) divide by 2
A = (b1 + b2) x h 2
Formulas You Need To Know
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Finding Area - Triangles
Area = b x h 5 cm x 8 cm = 40 cm2 = 20 cm2 2 2 2
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Area = b x h 6 cm x 6 cm = 36 cm2 = 18 cm2 2 2 2
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Area = b x h 10 cm x 5 cm = 50 cm2 = 25 cm2 2 2 2
4in
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Finding Area - Parallelograms
A = b x h 10.3 cm x 6.2 cm = 63.86 cm2
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A = b x h 10 cm x 3 cm = 30 cm2
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A = b x h 8 cm x 6 cm = 48 cm2
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Finding Area - Trapezoids
A = (b1 + b2) x h 1) 4 ft + 6 ft = 10 ft 2 2) 10 ft x 2 ft = 20 ft2
3) 20 ft2 ÷ 2 = 10 ft2
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A = (b1 + b2) x h 1) 2 ft + 4 ft = 6 ft
2 2) 6 ft x 5 ft = 30 ft2
3) 30 ft2 ÷ 2 = 15 ft2
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A = (b1 + b2) x h 1) 7 ft + 8 ft = 15 ft
2 2) 15 ft x 4 ft = 60 ft2
3) 60 ft2 ÷ 2 = 30 ft2
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Composite Polygons
A Composite Polygon is an irregular polygon made up of different
polygons.
To find the AREA OF A COMPOSITE POLYGON, first break the polygon into
simpler parts.
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Finding Area – Composite Polygon
This shape breaks down into these two
shapes.
So… find the area of each of the two areas separately and add the areas
together.
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Find the Area…
Area of Part A: 1.7 cm x 4.9 cm = 8.33 cm2
Area of Part B: 2.1 cm x 1.3 cm = 2.73 cm2
The Composite Polygon’s Area is the total of the two parts:
8.33 cm2 + 2.73 cm2 = 11.06 cm2
Part A
Part B
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Net Figures – Total Surface Area
Total Surface Area Find the area of each shape
separately, then add the areas together.
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3
24 56
Finding Total Surface Area
AREA OF RECTANGLE 1: 3 CM X 2 CM = 6 CM2
AREA OF RECTANGLE 2: 6 CM X 2 CM = 12 CM2
AREA OF RECTANGLE 3: 3 CM X 2 CM = 6 CM2
AREA OF RECTANGLE 4: 6 CM X 2 CM = 12 CM2
AREA OF RECTANGLE 5: 3 CM X 6 CM = 18 CM2
AREA OF RECTANGLE 6: 3 CM X 6 CM = 18 CM2
TOTAL SURFACE AREA: 6 + 12 + 6 + 12 + 18 + 18 = 96 CM2
1
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FINDING VOLUME
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You Only Need One Formula
Area of Base x Height of Prism
The triangle is the BASE of the
Prism
Height of Prism
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Follow These Steps…
1) Identify the shape of the base: Triangle
2) What is the formula for area for that shape:
(b x h) / 2
3) What is the area of the base: (7 x 8) / 2 = 56/2 = 28
4) What is the height of the prism: 13
5) What is the formula for volume: area of base x height of prism
6) What is the volume of the prism: 28 x 13 = 364
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Follow These Steps…
Identify the shape of the base: Square
2) What is the formula for area for that shape:
b x h
3) What is the area of the base: 3 cm x 5 cm = 15 cm2
4) What is the height of the prism: 4 cm
5) What is the formula for volume: area of base x height of prism
6) What is the volume of the prism: 15 cm2 x 4 cm = 60 cm3