Make a copy of this table. Assuming each figure is a regular polygon, find the missing value. Round answers to the nearest tenth where appropriate. Polygon Side length (cm) Apothem Area (cm 2 ) pentagon 6 61.9 hexagon 10 259.8 octagon 5 82.8 decagon 20 3077.7 hexagon 12 498.8 pentagon 30 3269.4

Given table: Polygon Side length (cm) Apothem Area (cm 2 ) pentagon 6 61.9 hexagon 10 259.8 octagon 5 82.8 decagon 20 3077.7 hexagon 12 498.8 pentagon 30 3269.4 Here, we have to find the different parameters in the given table in the blank space. The general formula of a regular polygon: A r e a o f p o l y g o n = n u m b e r o f s i d e × 1 2 × A p o t h e m × s i d e l e n g t h We use this formula to find different parameters. Let take rows of table one by one to find the value of blank space. Row1: It is a pentagon means it has 5 sides. We have to find apothem. A r e a o f p o l y g o n = n u m b e r o f s i d e × 1 2 × a p o t h e m × s i d e l e n g t h 61 . 9 = 5 × 1 2 × a p o t h e m × 6 A p o t h e m = 61 . 9 × 2 5 × 6 A p o t h e m = 4 . 1 c m Row2: It is a hexagon means it has 6 sides. We have to find apothem. A r e a o f p o l y g o n = n u m b e r o f s i d e × 1 2 × a p o t h e m × s i d e l e n g t h 259 . 8 = 6 × 1 2 × a p o t h e m × 10 A p o t h e m = 259 . 8 × 2 6 × 10 A p o t h e m = 8 . 7 c m Row3: It is an octagon means it has 8 sides. We have to find side length. A r e a o f p o l y g o n = n u m b e r o f s i d e × 1 2 × a p o t h e m × s i d e l e n g t h 82 . 8 = 8 × 1 2 × 5 × s i d e l e n g t h S i d e l e n g t h = 82 . 8 × 2 8 × 5 S i d e l e n g t h = 4 . 1 c m Row4: It is a decagon means it has 10 sides. We have to find apothem. A r e a o f p o l y g o n = n u m b e r o f s i d e × 1 2 × a p o t h e m × s i d e l e n g t h 3077 . 7 = 10 × 1 2 × a p o t h e m × 20 A p o t h e m = 3077 . 7 × 2 10 × 20 A p o t h e m = 30 . 8 c m Row5: It is a hexagon means it has 6 sides. We have to find side length. A r e a o f p o l y g o n = n u m b e r o f s i d e × 1 2 × a p o t h e m × s i d e l e n g t h 498 . 8 = 6 × 1 2 × 12 × s i d e l e n g t h S i d e l e n g t h = 498 . 8 × 2 6 × 12 S i d e l e n g t h = 13 . 9 c m Row6: It is a pentagon means it has 5 sides. We have to find side length. A r e a o f p o l y g o n = n u m b e r o f s i d e × 1 2 × a p o t h e m × s i d e l e n g t h 3269 . 4 = 5 × 1 2 × 30 × s i d e l e n g t h S i d e l e n g t h = 3269 . 4 × 2 5 × 30 S i d e l e n g t h = 43 . 6 c m Now we fill the table. Polygon Side length (cm) Apothem (cm) Area (cm 2 ) Pentagon 6 4.1 61.9 Hexagon 10 8.7 259.8 Octagon 4.1 5 82.8 Decagon 20 30.8 3077.7 Hexagon 13.9 12 498.8 Pentagon 43.6 30 3269.4

HARD

MYP:2

IMPORTANT

Earn 100

Find the perimeter and area of the following polygon. Round your answer to the nearest tenth.

Important Questions on 2D and 3D Geometry Human and Natural Landscapes

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MYP:2

IMPORTANT

MYP Mathematics A concept-based approach 2>Chapter 5 - 2D and 3D Geometry Human and Natural Landscapes>Practice 1>Q 1

Find the perimeter and area of the following polygon. Round your answer to the nearest tenth.

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MYP:2

IMPORTANT

MYP Mathematics A concept-based approach 2>Chapter 5 - 2D and 3D Geometry Human and Natural Landscapes>Practice 1>Q 1

Find the perimeter and area of the following polygon. Round your answer to the nearest tenth.

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IMPORTANT

MYP Mathematics A concept-based approach 2>Chapter 5 - 2D and 3D Geometry Human and Natural Landscapes>Practice 1>Q 2

Show that the area of a square calculated using the apothem is the same as the area using the standard formula.

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MYP:2

IMPORTANT

MYP Mathematics A concept-based approach 2>Chapter 5 - 2D and 3D Geometry Human and Natural Landscapes>Practice 1>Q 3

Make a copy of this table. Assuming each figure is a regular polygon, find the missing value. Round answers to the nearest tenth where appropriate.

Polygon	Side length (cm)	Apothem	Area (cm²)
pentagon	6		61.9
hexagon	10		259.8
octagon		5	82.8
decagon	20		3077.7
hexagon		12	498.8
pentagon		30	3269.4

MEDIUM

MYP:2

IMPORTANT

MYP Mathematics A concept-based approach 2>Chapter 5 - 2D and 3D Geometry Human and Natural Landscapes>Practice 1>Q 4

The Rich-Twinn Octagon House is a historic house in Akron, New York, and is on the National Register of Historic Places.

Sketch a diagram of the floor plan for the ground floor.

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MYP:2

IMPORTANT

MYP Mathematics A concept-based approach 2>Chapter 5 - 2D and 3D Geometry Human and Natural Landscapes>Practice 1>Q 4

The Rich-Twinn Octagon House is a historic house in Akron, New York, and is on the National Register of Historic Places. The area of the floor plan is $120.7 m^{2}$ and its perimeter measures $40 m$ . Find the apothem of the octagonal floor plan.

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MYP:2

IMPORTANT

MYP Mathematics A concept-based approach 2>Chapter 5 - 2D and 3D Geometry Human and Natural Landscapes>Practice 2>Q 1

Find the circumference and area of the following circles. Use $3.14$ for the value of $π$ , and round your answers to the nearest hundredth.

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