Knowing how to find the area of quadrilaterals is a basic knowledge required in making mathematical measurements. Quadrilateral is a polygon with four sides. It is sometimes referred to as a square or a square. Usually the four vertices are considered to be on the same plane. However, if they are not on the same plane, one speaks of a crooked square.

Quadrilaterals are divided into three categories based on the location of the vertices and sides. If all external angles of a quadrilateral are reflex angles, one speaks of a convex quadrilateral. If one of the outer angles of a quadrilateral is not a reflex angle, that quadrilateral is a concave quadrilateral. If the sides of the square intersect at the appointment, it is called a crossed square.

Some squares with regular shapes are listed below.

The area of each shape can be determined using the formulas in the following section.

Square, rectangle, diamond, and diamond are all parallelograms. Hence their opposite sides are parallel and equal. The square has all the same sides and all interior angles as right angles, and the rectangle has unequal adjacent sides, but all interior angles are right angles. Rhombus has equal sides with sloping interior angles. With the rhombus, not only are the adjoining sides different and the interior angles oblique.

Trapezoid is not a parallelogram and only two of the sides are parallel. Parallel sides are of unequal length and the distance between the parallel sides is considered the height of the trapezoid.

## Find the area of the quadrangles - area formulas

To find the area of the square, only the length of one side is needed, and for the rectangle, the lengths of both sides are needed.

### Square area - formula

Area of a square _{ } = *a* ^{2} where a is the length of the sides

### Area of a rectangle - formula

Area of a rectangle = *a* × *b* where *a* and *b are* the lengths of the rectangles

### Area of a diamond - formula

Both rhombus and rhomboid require the length of one side and the vertical height from that side.

Area of a diamond = *a* × *h* where *a* and *h are* the side length and the height of the diamond

Area of a diamond = *a* × *h* where a and *h are* the side length and the height of the diamond

### Area of a trapezoid - formula

For trapezoid, the length of the two parallel sides and the vertical height are required.

Area of a trapezoid = ½ ( *a* + *b* ) × *h* where *a* and *b are* the length of the two parallel sides and *h is* the vertical height

## Find the area of the squares - examples

- The side length of a square is 10 cm. Find the area of the square.

With the square are formulas

A _{square} = *a* ^{2} = 10 ^{2} = 100cm ^{2}

- A property is 700 m long and 120 m wide, what is the total area of the property?

With the rectangular area formula

A _{rectangle} = *a* × *b* = 700 × 120 = 84000 m ^{2}

- A diamond has sides that are 5 cm long and two adjacent sides form an angle of 30 degrees. What is the area of the diamond?

With the diamond area formula

A _{rhombus} = *a* × *h* = 5 × 5sin 30 ^{0} = 12.5m ^{2}

- A rhomboid has sides that are twice as wide. When the figure is 24 cm in circumference and it forms a pair of 120
^{°}interior angles, find the area of the diamond.

The length of the sides is not given, but a relationship between the length and the width and the circumference is given. Therefore we can derive the side length from it.

If width is *x* , then length is 2 *x* . Then the circumference is *x* + 2 *x* + *x* + 2 *x* = 24, and the solution is *x* = 4 cm.

Since the diamond forms an angle of 120 ^{0} at a vertex, the area is

With the diamond area formula

A _{rhomboid} = *a* × *h* = 4 × 4sin (180 ^{0} -120 ^{0} ) = 4 × 4 × √3 / 2〗 = 8√3 = 8 × 1.73 = 13.85cm ^{2}