**Area of quadrilaterals :**

A quadrilateral is a flat shape with four straight sides.

Types of quadrilaterals :

- Square
- Rectangle
- Parallelogram
- Rhombus
- Trapezium

A square has got 4 sides of equal length and 4 right angles (right angle = 90 degrees). |
A Rhombus has got 4 sides of equal length and opposite sides are parallel and angles are equal. | |

The rectangle (oblong) contains 4 right angles (an angle of 90˚). It has got 2 pairs of equal sides and 4 right angles |
A parallelogram is a rectangle that has been pushed over. Opposite sides are the same length and they are parallel. | |

Area of square = 4a

Area of rectangle = Length x width

Area of parallelogram = base x height

Area of rhombus = (1/2) x (d₁ x d₂)

Area of trapezium = (1/2) x h (a+ b)

**Example 1 :**

A window shaped like a parallelogram has an area of 18 ⅓ square feet. The height of the window is 3 ⅓ feet. How long is the base of the window?

**Solution :**

Area of the parallelogram = base x height

Area of window = 18 ⅓ square feet

height of window = 3 ⅓

Let "x" be the base of the parallelogram

x **x **3 ⅓ = 18 ⅓

x **x **10/3 = 55/3

x = (55/3) **x** (3/10)

x = 11/2

x = 5 ½ feet

Hence, the length of window is 5 ½ feet.

**Example 2 :**

A section in a stained glass window is shaped like a trapezoid. The top base is 4 centimeters and the bottom base is 2.5 centimeters long. If the area of the section of glass is 3.9 square centimeters, how tall is the section?

**Solution :**

Area of the trapezoid = (1/2) x h (a + b)

length of top base (a) = 4 cm

length of bottom base = 2.5 cm

Area of the section = 3.9 square centimeters

(1/2) x h (4 + 2.5) = 3.9

(1/2) x h (6.5) = 3.9

h = (3.9 x 2) / 6.5

h = 1.2 cm

**Example 3 :**

A parallelogram-shaped field in a park needs sod. The parallelogram has a base of 21.5 meters and a height of 18 meters. The sod is sold in pallets of 50 square meters. How many pallets of sod are needed to fill the field?

**Solution :**

Base length of the park = 21.5 m

height = 18 m

Area of parallelogram shaped field = base x height

= 21.5 x 18

= 387

Number of pallets required to fill the field = 387/50

= 7.74

Hence 8 pallets are needed to fill the field.

- Area and polygons
- Inverse operations
- Area of square and rectangles
- Area of quadrilaterals
- Area of a parallelogram
- Finding the area of a trapezoid
- Finding the area of a rhombus
- Area of triangles
- Finding the area of a triangle
- Problems using area of a triangles
- Solving area equations
- Writing equations using the area of a trapezoid
- Solving multistep problems
- Area of polygons
- Finding areas of polygons
- Real world problems involving area and perimeter of polygon

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