Assuming each figure is a regular polygon, find the missing values in the following table. Round answers to the nearest tenth where necessary. Polygon Side length (cm) Apothem (cm) Area (cm 2 ) Pentagon 9 92 . 3 Hexagon 10 144 Octagon 24 672 . 5 Decagon 8 1200

Given table: Polygon Side length (cm) Apothem (cm) Area (cm 2 ) Pentagon 9 92 . 3 Hexagon 10 144 Octagon 24 672 . 5 Decagon 8 1200 In the table, we have to find different values in different rows. To find these values we use the general formula of a regular polygon. Area of a regular polygon = 1 2 × Perimeter × apothem We take rows one by one to find the missing value. Row 1 : Here the given polygon is pentagon which means it has five sides. We have to find apothem. Area of pentagon = 1 2 × 5 × side length × apothem 92 . 3 = 5 × 1 2 × 9 × apothem apothem = 92 . 3 × 2 5 × 9 apothem = 4 . 1 cm So, the value of apothem in row1 is 4 . 1 cm . Row 2 : Here the given polygon is a hexagon which means it has six sides. We have to find side length. Area of hexagon = 1 2 × 6 × side length × apothem 144 = 1 2 × 6 × side length × 10 side length = 144 × 2 6 × 10 side length = 4 . 8 cm So, the value of side length in row2 is 4 . 8 cm . Row 3 : Here the given polygon is octagon which means it has eight sides. We have to find the apothem. Area of octagon = 1 2 × 8 × side length × apothem 672 . 5 = 1 2 × 8 × 24 × apothem apothem = 672 . 5 × 2 8 × 24 apothem = 7 . 0 cm So, the value of apothem in row 3 is 7 . 0 cm . Row 4 : Here the given polygon is decagon which means it has ten sides. We have to find the side length. Area of decagon = 1 2 × 10 × side length × apothem 1200 = 1 2 × 10 × side length × 8 side length = 1200 × 2 10 × 8 side length = 30 cm So, the value of side length in row 4 is 30 cm . Now, we fill the missing value in the table. Polygon Side length (cm) Apothem (cm) Area (cm 2 ) Pentagon 9 4 . 1 92 . 3 Hexagon 4 . 8 10 144 Octagon 24 7 672 . 5 Decagon 30 8 1200

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

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Earn 100

Find the perimeter and area of this shape.

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

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IMPORTANT

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

Find the perimeter and area of these shape.

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

Assuming each figure is a regular polygon, find the missing values in the following table. Round answers to the nearest tenth where necessary.

Polygon	Side length (cm)	Apothem (cm)	Area (cm²)
Pentagon	$9$		$92.3$
Hexagon		$10$	$144$
Octagon	$24$		$672.5$
Decagon		$8$	$1200$

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

Antonio Gaudi was one of the most celebrated architects in Spain, designing houses, churches and even sidewalks. In many parts of Barcelona, you will find sidewalks that he designed in 1904 to represent what it would be like to walk on the bottom of the ocean, complete with shells, starfish and seaweed.

Each of Gaudi's tiles is a regular hexagon with sides measuring 20 cm and an apothem of 17.3 cm.

Find the area of a single tile. Show your working.

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