Perimeter and Area of 2D Shapes
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Perimeter and Area of 2D Shapes — Free MYP5 Mathematics (Standard) Practice Questions

1QuestionUsing Compound Shapes in Area CalculationsConcept Practice
3 marks~5 minCriterion C
A compound shape consists of a rectangle of fixed length 10 cm and variable width ww cm, with a semicircle of diameter ww attached to one of the longer sides. The total area is given by

A=10w+πw28A = 10w + \frac{\pi w^2}{8}

The graph shows AA (cm²) against ww (cm) for 0≤w≤120 \leq w \leq 12.
a
Use the graph to estimate the total area when w=6w = 6 cm. [1]
b
Calculate the exact total area when w=6w = 6 cm. [1]
c
A designer requires the total area to be no greater than 150 cm². Use the graph to find the maximum possible width ww, then advise the designer on whether a width of 11 cm satisfies the constraint. [1]
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2QuestionArea of Trapeziums and RhombusesAssessment Practice
5 marks~8 minCriterion B
A landscape architect is designing a trapezoidal flower bed with parallel sides of length aa (top) and bb (bottom), where b>ab > a, and perpendicular height hh.
a
Construct a clearly labelled diagram showing the trapezium decomposed into one rectangle and two right-angled triangles. Label the parallel sides aa and bb, the height hh, and the horizontal bases of the two triangles xx (left) and yy (right). [1]
b
Using your diagram, justify that x+y=b−ax + y = b - a, write algebraic expressions for the area of each component shape, and show that their sum simplifies to A=12(a+b)hA = \frac{1}{2}(a+b)h. [3]
c
The architect states that a trapezoidal bed with a=3a = 3 m, b=7b = 7 m, and h=4h = 4 m has sufficient area to plant 20 lavender bushes, each requiring at least 0.90.9 m² of space. Assess whether the architect's claim is correct. [1]
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3QuestionArea of Trapeziums and RhombusesConcept Practice
4 marks~6 minCriterion A
A landscape architect is designing a trapezoidal garden bed. On a coordinate grid (1 unit = 1 m), the bed is modelled by trapezium ABCDABCD with vertices A(1,1)A(1, 1), B(7,1)B(7, 1), C(5,5)C(5, 5), and D(3,5)D(3, 5), where AB∥CDAB \parallel CD.
a
Calculate the lengths of ABAB and CDCD, and the perpendicular height hh of the trapezium. [2]
b
Using A=12(a+b)hA = \frac{1}{2}(a + b)h, calculate the area of the garden bed. [1]
c
The architect states that a garden bed smaller than 18 m² is too small for the planned planting scheme. Advise the architect whether this garden bed is suitable for the planting scheme. [1]
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4QuestionArea of Rectangles Triangles and ParallelogramsAssessment Practice
5 marks~8 minCriterion D
A homeowner plans to tile a rectangular deck measuring 6 m by 4 m, with a right-angled triangular extension attached to one of the 4 m sides. The triangle has a base of 4 m and a perpendicular height of 2 m. The homeowner purchases exactly 28 m² of tiles, based on the total deck area alone.

The tile installer states that a 5% waste factor for cutting and breakage must be added to any area calculation before purchasing.
a
Calculate the total area of tiles that should have been purchased, including the 5% waste factor. [2]
b
Advise the homeowner whether the 28 m² purchased is sufficient for this tiling project, justifying your answer with reference to both the mathematics and the practical limitations of the area model used. [3]
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