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General Mathematics Β· Unit 1 Β· Shape and measurement Β· Mensuration

Calculate areas, 𝐴, of standard two-dimensional objects in practical situations, including circles, sectors of circles, triangles, rectangles, parallelograms, trapeziums and composites. ο‚§ circle: 𝐴 = πœ‹π‘Ÿ2 where π‘Ÿ is radius ο‚§ sector: 𝐴 = πœƒ 360 πœ‹π‘Ÿ2 where πœƒ is central angle and π‘Ÿ is radius ο‚§ triangle: 𝐴 = 1 2 π‘β„Ž where 𝑏 is base length and β„Ž is perpendicular height ο‚§ parallelogram: 𝐴 = π‘β„Ž where 𝑏 is base length and β„Ž is perpendicular height ο‚§ trapezium: 𝐴 = 1 2 (π‘Ž + 𝑏)β„Ž where π‘Ž and 𝑏 are parallel lengths and β„Ž is perpendicular height

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Question 1

A landscape architect is designing a decorative paving feature for a community park. The design consists of a rectangular base measuring 12.0 m by 8.0 m, with semicircular sections of radius 4.0 m removed from two opposite sides. Calculate the total area of paving material required, in square metres, correct to one decimal place.

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Question 2

A decorative garden bed is composed of a rectangular section and a semicircular section joined together. The rectangle has dimensions $12 \text{ m}$ (length) by $5 \text{ m}$ (width). The semicircle is attached to one of the shorter ends of the rectangle and has a diameter equal to the width of the rectangle. a) Calculate the area of the rectangular section. (1 mark) b) Calculate the area of the semicircular section. (1 mark) c) Calculate the total area of the garden bed, correct to 1 decimal place. (1 mark)

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Calculate perimeters, 𝑃, of standard two-dimensional objects in practical situations, including circles, sectors, triangles, rectangles, trapeziums, parallelograms and composites. ο‚§ circle: 𝐢 = 2πœ‹π‘Ÿ where 𝐢 is circumference and π‘Ÿ is radius ο‚§ sector: 𝑃 = 2π‘Ÿ + πœƒ 180 πœ‹π‘Ÿ where πœƒ is central angle and π‘Ÿ is radius General Mathematics 2025 v1.3
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