Geometric Figure Calculations and Strategies
Various geometric figures composed of circles, rectangles, squares, triangles, and semicircles are analyzed to find the area, perimeter, and total area of shaded parts using different strategies. Formulas and step-by-step calculations are provided with the results rounded off to the nearest whole number.
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The figure is made up of 3 semicircles and a right-angled triangle. Find the area of the shaded part, rounding off your answer to the nearest whole number.
Strategy : Small semi circle + Medium semi circle + triangle Big semi circle 2x x 2.5 x 2.5 + 1 1 2x x 6.5 x 6.5 1 2x x 6 x 6 + 1 Area 2 x 5 x 12 = 3.125 + 18 + 30 21.125 = 30
The figure is made up of a rectangle, a square and a quadrant. Find the area of the shaded part, rounding off your answer to the nearest whole number.
Strategy : Rectangle corner (square quad) triangle 20 x 8 (8 x 8 1 4x x 8 x 8) 1 Area 2 x 20 x 8 = 160 (64 16 ) 80 = 16 + 16 66 (nearest whole number)
The figure shows a shaded part bounded by 2 quadrants. Calculate the area and perimeter of the shaded part, rounding off your answer to the nearest whole number.
Strategy : Area 1 Square (cut & paste) Area = 64 8 x 8
Strategy : Perimeter Semi circle + 2 radii (rotation quad) 1 Perimeter = 8 + 16 41 (nearest whole number) 2x 2 x x 8 + 2 x 8
The figure is made up of a semi-circle and an isosceles triangle of side 16 cm. Find the total area of the shaded parts, rounding off your answer to the nearest whole number.
Strategy : half triangle (cut & paste) 1 2 x 1 Area 2 x 16 x 16 = 64
The figure shows 3 different squares and a semicircle with centre O. If the diameter of the semicircle is 20 cm, find the perimeter of the figure, rounding off your answer to the nearest whole number
Strategy : Semi circle + 4 radii (pop out) 1 Perimeter 2 x 2 x x 10 + 4 x 10 = 10 + 40 71
Find the area of the shaded part rounding your answer to the nearest whole number.
Strategy : 1 rectangle (cut & paste) Area = 162 18 x 9
The figure below is formed by using a big semicircle and 3 small semi-circles with radii of 30 cm and 10 cm respectively. Find the perimeter and area of the shaded part. Round off your answers to the nearest whole number.
Strategy : Perimeter Big Semi circle + 3 Small Semi circles 1 2x 2 x x 30 + 3 x 1 Perimeter = 30 + 30 = 60 188 (nearest whole number) 2x 2 x x 10
Strategy : Area Big Semi circle 3 Small Semi circles 2 x x 30 x 30 3 x 1 = 450 150 = 300 942 (nearest whole number) 1 Area 2 x x 10 x 10
Find the perimeter and area of the shaded part, rounding your answers to the nearest whole number.
Strategy : Perimeter Big Circle + 2 radii Perimeter = 10 + 10 41 (nearest whole number) 2 x x 5 + 2 x 5
Strategy : Area Square Circle (cut & paste) Area = 100 25 21 (nearest whole number) 10 x 10 x 5 x 5
Strategy : 1 Perimeter 4 Big Circle + Small Circle 1 Perimeter = 7 + 14 66 (nearest whole number) 4 x 2 x x 14 + 2 x x 7
Strategy : Area Quarter Circle Triangle 4x 14 x 14 1 = 49 98 56 (nearest whole number) 1 Area 2 x 14 x 14
