Compound Shapes and Nets

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Compound Shapes and Nets — Free MYP3 Mathematics Practice Questions

1QuestionArea and Perimeter of Compound ShapesConcept Practice

2 marks~3 minCriterion A

The diagram shows a compound shape made from a rectangle and a semicircle. The rectangle has a length of 10 cm and a width of 6 cm. The semicircle is attached to one of the 6 cm sides.

Calculate the radius of the semicircle. [1]

Explain how many sides of the rectangle form part of the perimeter of the compound shape. [1]

Solutions

2QuestionBreaking Down Compound Shapes into Simple PartsAssessment Practice

3 marks~5 minCriterion C

The table below shows the side length and area of a square.

Side length $s$ (cm)	0	1	2	3	4	5
Area $A$ (cm²)	0	1	4	9	16	25

State the formula that connects the side length

s

and the area

A

of a square. [1]

Explain why the graph of this relationship is a curve rather than a straight line. [1]

A student claims: "If the side length doubles, the area also doubles." Analyse this claim using values from the table. [1]

Solutions

3QuestionDrawing and Interpreting Nets of 3D ShapesAssessment Practice

6 marks~9 minCriterion B

A right prism has a regular pentagonal base with side length 4 cm and height 10 cm.

The area of a regular polygon with

n

sides of length

s

A = \dfrac{ns^2}{4\tan(\pi/n)}

Calculate the lateral surface area of the pentagonal prism. [2]

Calculate the area of one pentagonal base. Show your working. [2]

A student claims: "The more sides the base has, the greater the total surface area." Using your results and the total surface areas of a triangular prism (

\approx 133.9\ \text{cm}^2

) and a hexagonal prism (

\approx 323.1\ \text{cm}^2

), all with side length 4 cm and height 10 cm, analyse whether this claim is correct. [2]

Solutions

4QuestionArea and Perimeter of Compound ShapesAssessment Practice

6 marks~9 minCriterion D

A gardener plans two overlapping rectangular flower beds and needs to find the total area to calculate the volume of soil required at a uniform depth of

0.3 \, \text{m}

.

Bed A:

4 \, \text{m} \times 3 \, \text{m}

Bed B:

5 \, \text{m} \times 2 \, \text{m}

Overlapping region:

2 \, \text{m} \times 1 \, \text{m}

Calculate the total area of the two flower beds combined. [2]

Calculate the total volume of soil required. [1]

The gardener's model assumes perfectly rectangular beds and a uniform soil depth of

0.3 \, \text{m}

. Explain two reasons why this model may not accurately predict the actual volume of soil needed in a real garden. [3]

Solutions

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