triangles, quadrilaterals, nets, prisms & composite polygons
TRANSCRIPT
Finding Area & Volume
Triangles, Quadrilaterals, Nets, Prisms & Composite Polygons
Formulas You Need To Know
PARALLELOGRAM
A = b x h 2
A = b x h
TRIANGLE
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
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
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
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
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.
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.
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
Net Figures – Total Surface Area
Total Surface Area Find the area of each shape
separately, then add the areas together.
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
FINDING VOLUME
You Only Need One Formula
Area of Base x Height of Prism
The triangle is the BASE of the
Prism
Height of Prism
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
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