Survey Plot

Find the exact area of the polygon.

Area = sq. unitsL

(𝑥1 , 𝑦 1 )

(𝑥2 , 𝑦2 )

(𝑥3 , 𝑦3 )

𝒙

𝒚

What’s the area of this triangle?

(𝑥1 , 𝑦 1 )

(𝑥2 , 𝑦2 )

(𝑥3 , 𝑦3 )

𝒙

𝒚

What’s the area of this triangle?

(𝑥1 , 𝑦 1 )

(𝑥2 , 𝑦2 )

(𝑥3 , 𝑦3 )

(𝑥1 ,0 ) (𝑥2 ,0 ) (𝑥3 ,0 )𝒙

𝒚

What’s the area of this triangle?

(𝑥1 , 𝑦 1 )𝟏𝟐 (𝒚𝟐+𝒚𝟏 ) ( 𝒙𝟐− 𝒙𝟏 )

𝟏𝟐 (𝒚𝟑+𝒚𝟐 ) ( 𝒙𝟑− 𝒙𝟐 ) 𝟏

𝟐 (𝒚𝟑+𝒚𝟏 ) ( 𝒙𝟑− 𝒙𝟏 )

(𝑥1 , 𝑦 1 )𝟏𝟐 (𝒚𝟐+𝒚𝟏 ) ( 𝒙𝟐− 𝒙𝟏 )

𝟏𝟐 (𝒚𝟑+𝒚𝟐 ) ( 𝒙𝟑− 𝒙𝟐 ) 𝟏

𝟐 (𝒚𝟏+𝒚𝟑 ) ( 𝒙𝟏− 𝒙𝟑 )

So, list the coordinates in columns in a spreadsheet, repeating the first coordinates at the end.Then enter a formula for the area of the trapezium formed by the first pair of coordinates.Copy down this formula to the last point (point 3).Finally, sum the areas of the trapezium.

Point

Trapezium area

1

2

3

1

Total

So, list the coordinates in columns in a spreadsheet, repeating the first coordinates at the end.Then enter a formula for the area of the trapezium formed by the first pair of coordinates.Copy down this formula to the last point (point 3).Finally, sum the areas of the trapezium.

Point

Trapezium area

1

2

3

1

Total

So, list the coordinates in columns in a spreadsheet, repeating the first coordinates at the end.Then enter a formula for the area of the trapezium formed by the first pair of coordinates.Copy down this formula to the last point (point 3).Finally, sum the areas of the trapezium.

Point

Trapezium area

1

2

3

1

Total

So, list the coordinates in columns in a spreadsheet, repeating the first coordinates at the end.Then enter a formula for the area of the trapezium formed by the first pair of coordinates.Copy down this formula to the last point (point 3).Finally, sum the areas of the trapezium.

Point

Trapezium area

1

2

3

1

Total

What if the polygon had a hole in it?

Think of this point as point 4 in the list.

hole

A

D

B

C

F

E

H

G

I

JK

L

M

N

O

Q P

R

S

So to include a hole insert its co-ordinates into the existing list taking care to repeat connecting points (i.e. J and K) and avoid crossing over previous lines.

RESOURCES

Find the exact area of the polygon.

Area = sq. unitsA

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Find the exact area of the polygon.

Area = sq. unitsB

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Find the exact area of the polygon.

Area = sq. unitsC

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Find the exact area of the polygon.

Area = sq. unitsD

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Find the exact area of the polygon.

Area = sq. unitsE

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Find the exact area of the polygon.

Area = sq. unitsF

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Find the exact area of the polygon.

Area = sq. unitsG

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Find the exact area of the polygon.

Area = sq. unitsH

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Find the exact area of the polygon.

Area = sq. unitsI

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Find the exact area of the polygon.

Area = sq. unitsJ

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Find the exact area of the polygon.

Area = sq. unitsK

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Find the exact area of the polygon.

Area = sq. unitsL

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Find the exact area of the polygon.

Area = sq. unitsM

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Find the exact area of the polygon.

Area = sq. unitsN

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