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9 Measurement
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AustraliaNSW
Stage 4

9.01 Areas of special quadrilaterals

Lesson
Worksheet
Practice

Interactive practice questions

If this parallelogram is cut along the dotted line, the pieces can be rearranged to form a rectangle:

A parallelogram with a width of 9 cm and a vertical height of 6 cm as indicated by a dashed line. This dashed line cuts the parallelogram into two shapes. A right trapezoid (colored brown) with a longer base on top and a shorter base on the bottom, and a right-angled triangle (colored green). The green right-angled triangle is from the left side of the parallelogram and the right trapezoid is the remaining shape. The green right-angled triangle is flipped horizontally and repositioned to the right side of the right trapezoid to form a rectangle. This rectangle has a longer width labeled 9 cm and a height of 6 cm.
a

Complete the table to find the area of the rectangle.

$\text{Area of rectangle }$Area of rectangle $=$= $\text{length }\times\text{width }$length ×width cm2
$A$A $=$= $\editable{}\times\editable{}$× cm2 (Fill in the values for the length and width)
$A$A $=$= $\editable{}$ cm2 (Complete the multiplication to find the area)
b

Now find the area of the parallelogram.

Easy
1min

The rhombus on the left can be split into two triangles as shown.

Easy
2min

Consider the rhombus shown on the left:

Easy
1min

Consider the trapezium shown below which has been split into a rectangle and a right-angled triangle.

Easy
2min
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Outcomes

MA4-12MG

calculates the perimeters of plane shapes and the circumferences of circles

MA4-13MG

uses formulas to calculate the areas of quadrilaterals and circles, and converts between units of area

MA4-17MG

classifies, describes and uses the properties of triangles and quadrilaterals, and determines congruent triangles to find unknown side lengths and angles

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