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Geometry Review and Reinforcement
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Geometry Review and Reinforcement
Help a hospital ward redesign its spaces and equipment. Show your working, include units, and use π = 3.14 unless told otherwise. Give answers to 1 decimal place where needed.
Geometry on the ward
Use angle facts, transformations and scale factors to check the redesign.
1.A straight corridor junction is split into angles of 4x° and 2x°. Find x and both angle sizes.
2.Two parallel edges of a tiled wall are crossed by a diagonal strip. One acute angle is 68°. What is the size of the corresponding angle? What is the size of the adjacent angle on a straight line?
3.A floor-plan symbol is translated 5 units right and 2 units down. Its original point is (−3, 4). What are the new coordinates?
4.A room plan is enlarged by scale factor 1.5. An original wall length is 4.8 m and the floor area is 32 m². Find the enlarged wall length and enlarged area.
Surfaces and space
Calculate carefully and state whether each result is a length, area or volume.
5.A circular observation window has radius 0.45 m. Calculate its area.
6.A storage crate is a rectangular prism measuring 0.8 m by 0.5 m by 0.6 m. Find its volume in cubic metres and litres. (1 m³ = 1000 L.)
7.A cylindrical oxygen canister has radius 7 cm and height 30 cm. Calculate its volume and its total surface area, including both circular ends.
8.A rectangular noticeboard is 2.4 m long and 1.2 m high. A semicircular panel with diameter 1.2 m is attached along one short side. Find the combined area.
Reason it out
Use geometry to make a design decision and explain your method.
9.A triangular sign has angles 2x°, (x + 20)° and (3x − 10)°. Find x and all three angles. Check that your angles form a triangle.
10.A technician says, “If every length on a box is doubled, its volume is doubled.” Is this correct? Explain what happens to the volume of a box originally measuring 3 cm × 4 cm × 5 cm.
11.A square equipment mat has area 81 m². What is its side length and perimeter?
3 printable pages
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