Area, surface area and volume
Try these fresh problems without your notes. Explain your method before opening a solution. This practice is not a graded school assessment.
Check 1
A triangle has base 7 cm and perpendicular height 6 cm. What is its area?
Check 2
A closed cube has side 3 cm. What is its total surface area?
Challenge 1
An open rectangular tray has internal base 5 cm by 4 cm and height 2 cm. Ignoring material thickness, find the inside surface area and capacity.
Show a hint
Count one base and four side faces; calculate volume separately.
Show the worked solution
Inside surface area 56 cm²; capacity 40 cm³ or 40 mL.
The base is 20 cm² and sides total 2 × 5 × 2 + 2 × 4 × 2 = 36 cm². Volume is 5 × 4 × 2 = 40 cm³. There is no lid.
Challenge 2
A rectangle has vertices (−3, −2), (3, −2), (3, 2), (−3, 2). A diagonal divides it into equal triangles. Find the area of either triangle.
Show a hint
Use coordinate differences to find the rectangle dimensions, then halve its area.
Show the worked solution
12 square units.
The rectangle is 6 units by 4 units, with area 24 square units. A diagonal splits it into two equal-area triangles, each of area 12.
Decide what to revisit
If a method was difficult to explain, return to that lesson and schedule a recall check. Unit-review answers are not saved as a score.
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