Chapter 7 — Practice examination

A park plans a path measuring 3 1/4 m. How many cm of walkway should its survey include? Explain the conversion factor.

Application-and-critique task: A land-surveying team measures a footpath at 1 4/5 m. How many cm of walkway should its survey include? Explain the conversion factor. Independently prepare a labeled metric-conversion ratio table; do not simply repeat the first application question’s computation. A student wrote this solution: “9/5 m = 9/500 cm; I divided when converting to the smaller unit.” Is that reasoning valid? Name the first incorrect step; demonstrate a corrected computation and independently check it.

A rectangular greenhouse floor measures 3/4 m by 1 m. How many square meters of flooring are required? Draw accurately proportioned side lengths.

Application-and-critique task: An indoor growing area measures 1 m by 1/4 m. How many square meters of flooring are required? Draw accurately proportioned side lengths. Independently prepare a proportionate area rectangle with square-unit labeling; do not simply repeat the first application question’s computation. A student wrote this solution: “1 m × 1/4 m = 1/4 m; I left the area in a linear unit.” Is that reasoning valid? Name the first incorrect step; demonstrate a corrected computation and independently check it.

A field is triangular with base 9 cm and a 5 cm PERPENDICULAR altitude inside its base segment. Calculate the area and explain why the sloping edge is irrelevant.

Application-and-critique task: A kite-panel template is triangular with base 4 cm and a 8 cm PERPENDICULAR altitude inside its base segment. Calculate the area and explain why the sloping edge is irrelevant. Independently prepare a triangle with an altitude perpendicular to its selected base; do not simply repeat the first application question’s computation. A student wrote this solution: “Triangle area = 4 × 8 = 32 cm². I omitted the factor one half.” Is that reasoning valid? Name the first incorrect step; demonstrate a corrected computation and independently check it.

A field is triangular with base 9 cm and a 8 cm PERPENDICULAR altitude outside its base segment. Calculate the area and explain why the sloping edge is irrelevant.

Application-and-critique task: An architectural window panel is triangular with base 8 cm and a 11 cm PERPENDICULAR altitude outside its base segment. Calculate the area and explain why the sloping edge is irrelevant. Independently prepare an obtuse triangle with the altitude extended outside the base segment; do not simply repeat the first application question’s computation. A student wrote this solution: “Triangle area = 8 × 11 = 88 cm². I omitted the factor one half.” Is that reasoning valid? Name the first incorrect step; demonstrate a corrected computation and independently check it.

A tiled courtyard covers a 15 m by 9 m rectangle, except for a 7 m by 5 m corner garden with NO tiling. How many square meters are tiled? Explain subtraction without overlap.

Application-and-critique task: A property designer calculates tiling for a courtyard covering a 11 m by 7 m rectangle, except for a 3 m by 4 m corner garden with NO tiling. How many square meters are tiled? Explain subtraction without overlap. Independently prepare a uniformly scaled outer rectangle and a separate corner-cutout sketch; do not simply repeat the first application question’s computation. A student wrote this solution: “The missing corner ADDS area: 11×7+3×4=89 m².” Is that reasoning valid? Name the first incorrect step; demonstrate a corrected computation and independently check it.

A rectangle is 4/5 m long and 1/2 m wide. Show exact partitions and area.

A 11 m by 6 m rectangle has a 2 m by 3 m right triangle removed. Area?