Exploring the area of special quadrilaterals

Lesson

A quadrilateral is a shape with $4$4 straight sides. We know about Rectangles and Squares already, but there are other quadrilaterals we need to be familiar with.

Parallelogram

A parallelogram is a shape with the specific geometric properties of

• opposite sides equal in length
• opposite sides parallel

Trapezium

A trapezium (sometimes called trapezoid) is a 2D shape with the specific geometric properties of

• $1$1 pair of opposite sides that are parallel

All of these are trapeziums

Kite

A kite is a 2D shape with the specific geometric properties of

• $2$2 pairs of adjacent sides that are equal
• $1$1 pair of equal angles

Of course the kite you fly around on a windy day is named after the geometric shape it looks like.

Kites can taken on many different shapes and sizes. Try moving points $A$A, $O$O and $D$D on this mathlet to make many kinds of kites.

Rhombus

A rhombus is a 2D shape with the specific geometric properties of

• all sides equal in length
• opposite sides parallel
• opposite angles equal
• diagonals bisect each other

You can play with this mathlet to make many kinds of rhombuses. It also shows that we only need $1$1 side length and $1$1 angle to create one.

Exploring the Areas of Special Quadrilaterals

As we already know how to find the area of rectangles and triangles, one way to find the area of parallelograms, trapeziums, kites or rhombuses, would be to break up these shapes into smaller components comprising of rectangles and triangles, or by manipulating the shapes to look like rectangles.

Worked Examples

QUESTION 1

Consider the following parallelogram.

1. If the parallelogram is formed into a rectangle, what would the length and width of the rectangle be?

 Length: $\editable{}$ mm Width: $\editable{}$ mm
2. Hence find the area of the parallelogram.

QUESTION 2

Consider the kite on the left.

1. If the kite is formed into the rectangle on the right, what would the length and width of the rectangle be?

 Length: $\editable{}$ cm Width: $\editable{}$ cm
2. Hence find the area of the kite.

QUESTION 3

Find the area of the trapezium by summing the areas of the triangle and rectangle that comprise it.