Perimeter and Area of 2D Shapes
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Perimeter and Area of 2D Shapes — Free MYP2 Mathematics Practice Questions

1QuestionArea of Rectangles Triangles and ParallelogramsConcept Practice
3 marks~5 minCriterion A
The diagram shows a rectangle divided into triangle A, parallelogram P, and triangle B. The rectangle has length 10 cm and height 6 cm. Triangles A and B each have base 5 cm and height 6 cm. Parallelogram P has base 5 cm and height 6 cm.
a
Calculate the areas of triangle A and triangle B. [1]
b
Calculate the area of parallelogram P. [1]
c
Describe the relationship between the area of the rectangle and the areas of triangle A, parallelogram P, and triangle B combined. [1]
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Solutions

2QuestionArea of Trapeziums and Compound ShapesAssessment Practice
4 marks~6 minCriterion D
A farmer has a field shaped like a trapezium (a quadrilateral with one pair of parallel sides). The parallel sides measure 80 m and 120 m, and the perpendicular height is 50 m. One non-parallel side curves slightly outward, making the true area larger than the trapezium model suggests.

Area of trapezium=12×(b1+b2)×h\text{Area of trapezium} = \frac{1}{2} \times (b_1 + b_2) \times h

where b1b_1 and b2b_2 are the parallel sides and hh is the perpendicular height.
a
Calculate the area of the field using the formula above. Show your working. [2]
b
Explain whether the trapezium formula overestimates or underestimates the true area of this field, and identify one real-world limitation of using a straight-sided shape to model a field with a curved boundary. [2]
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3QuestionFinding Perimeter of Irregular ShapesAssessment Practice
5 marks~8 minCriterion C
An L-shaped figure is formed by joining a vertical rectangle (width 33 cm, height 88 cm) to a horizontal rectangle (width 66 cm, height 33 cm), as shown.

A student calculates the perimeter by adding all sides of both rectangles separately: 3+8+6+3+3+8+6+3=383 + 8 + 6 + 3 + 3 + 8 + 6 + 3 = 38 cm.
a
Identify the six outer side lengths of the L-shaped figure. [1]
b
Calculate the correct perimeter of the L-shaped figure. Show your working. [2]
c
Explain why the student's method gives the wrong answer. [2]
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Solutions

4QuestionFinding Perimeter of Irregular ShapesAssessment Practice
12 marks~18 minCriterion B
The perimeters of the first three L-shaped polygons in a sequence are 12 cm, 16 cm, and 20 cm. Each grid square has a side length of 1 cm.
a
Identify the pattern in the perimeters and state the perimeter of the 4th and 5th shapes. [2]
b
On the grid provided, draw the 5th shape. Explain how your drawing follows the same pattern as the first three shapes. [4]
c
Calculate the perimeter of your 5th shape by adding each side length. Compare this value with your prediction from part (a). [6]
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Solutions

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