finding area & volume

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

__________________________________________________ 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