Q&A for How to Find the Area of a Quadrilateral

Yes. If you know the base and height of each triangle, you can just add the two areas together. It's not always possible, however, to know the bases and heights.

Calculate as follows: Area = base multiplied by height.

Assuming you're not given the angle(s), you either have to use a protractor or analyze the quadrilateral and use trigonometry.

If you know the central angle of the sector, divide that angle by 360°, then multiply the resulting fraction by πr². If you know the length of the sector's arc, you can multiply that length by the radius, then divide by 2.

If the slanted sides are equal, you can easily find the height using symmetry and the Pythagorean theorem. If you have four arbitrary sides, you can apply the same idea but will need to solve a system of quadratic equations. Choose variables for leftoverhang, rightoverhang and height, and get one linear and two quadratic equations relating them.

If the diagonals are perpendicular, use half the product. If they are not perpendicular, it's more complicated.

Without knowing any angles, you cannot find sides, perimeter or area.

A quadrilateral with perpendicular diagonals is a rhombus or a square. See Method 1 Step 4 above.

A square has a greater area than any other quadrilateral of the same perimeter.

If it's a regular quadrilateral, it's base multiplied by height. If it's not a regular quadrilateral, there is no applicable formula. Nevertheless, the area of an irregular quadrilateral can be calculated by means of geometry and/or trigonometry.

The side lengths do not by themselves determine the shape. The interior angles play a big role, too, so any formula would have to take the angles (or trig functions) into account.

Multiply those numbers together to get the area: (x - 8) (x + 8) = (x² - 64) square units.

No. You would have to know at least one angle. Even then, there is no simple formula for the area.

Side lengths are not sufficient information, even if you have all four of them. You need angles, or the length of a diagonal, or some other measurement to constrain the shape.

Start by drawing an L shape for two of the sides and the angle between them. The corner and the ends of the L fix 3 of the 4 vertices, and we know the distance from the 4th to each of the ends. So sketch a circle of the appropriate radius around each one. The 4th vertex lies on the intersection of those two circles. Typically there will be two possible locations for the 4th vertex, one for a convex quadrilateral and one for a concave one, and they don't have the same area. So no, not generally, but you can narrow the area down to two possibilities.

You do not have enough information to find the area. You would also have to know the length of the fourth side and the sizes of the included angles. Then you would use Method 4 above.

They are the three most basic trigonometric functions. Each is the ratio of the length of one side of a right triangle to the length of another side.

You would have to draw an accurate scaled diagram (map) of your property, subdivide the diagram into a rectangle and triangles, then calculate the areas of the subdivisions and add them together.

You would need more information, such as the lengths of the diagonals, the size of the angles or the height of the rhombus.

That is a rectangle with a length of 5 and a width of 1. So its area is (1)(5) = 5 square units.

The area cannot be calculated unless you also know the shape of the quadrilateral and the size of all the angles.

First you have to know the lengths of the sides. With an irregular quadrilateral, you have to subdivide it into rectangles and right triangles, then use trigonometry to find the angles in the triangle(s).

An irregular quad might well consist of a square and two triangles. It could be almost any combination of rectangles, squares and triangles. You just add all the areas together.

First you would have to know the lengths of the sides. Then you would subdivide the quadrilateral into rectangles and right triangles. Using the side lengths of the triangle(s), you would consult a trigonometry table to find the angles involved.

When working with an irregular pentagon, you would have to subdivide the shape into rectangles and triangles, and you'd need to know the dimensions of those subdivisions. Then calculate the areas of each subdivision and add them together.