You will need

- - the minimum data required to solve the problem, namely the length of each sides and diagonals of a Pentagon;
- calculator;
- - handle;
- - a sheet of paper.

Instruction

1

Carefully read the condition of the task. Guided by them, draw on a sheet of paper alleged the Pentagon.

2

Label the length of each of its sides.

3

Swipe in the Pentagon, two diagonals. Label the length of each diagonal.

4

Notice what happened as a result of the diagonals, and you will see that they divide the Pentagon into three distinct triangles.

5

Of the vertices of each triangle draw a height to the base.

6

Measure the length of the height lowered at the base for each triangle.

7

Determine the area of all three triangles using the formula given below:

S = ½ × H × a,

where S is the calculated

H – the height of each triangle;

a – length of base of triangle.

S = ½ × H × a,

where S is the calculated

**area**of the triangle;H – the height of each triangle;

a – length of base of triangle.

8

Calculate

**the area****of a Pentagon**by adding together the areas of these three triangles.Note

Remember that the right is the Pentagon, in which all sides and all angles are equal. If at least one side or angle is different from the other, the Pentagon is not considered correct, and its area cannot be calculated based on the simplified scheme.

Useful advice

The easiest way to find the area of a regular Pentagon. To do this, simply calculate the area of one of the triangles, and then multiply it by their number. Because the diagonal in the right Pentagon break it into triangles of the same area. Much easier task and in that case, if two angles of a Pentagon are straight. Enough to hold one diagonal which will divide the Pentagon into a triangle and a rectangle, the area which can be found quite simply. The sum of the calculated squares will equal the area of the Pentagon.

# Advice 2 : How to calculate the area of a polygon

A polygon is a geometric figure constructed by closing the polyline. There are several types of polygon, which differ depending on the number of vertices. The calculation is made for each polygon in certain ways.

Instruction

1

Multiply the lengths of the sides if you need to calculate the area of a square or rectangle. If you want to know the area of a right triangle, extend it to a rectangle to calculate its area and divide it into two.

2

Use to compute the area of polygons the following method, if the shape has interior angles greater than 180 degrees (a convex polygon), and all its vertices are in the mesh nodes coordinates and polyline itself does not cross.

Describe around such a polygon rectangle so that its sides were parallel to the grid lines (coordinate axes). At least one of the vertices of the polygon must be a vertex of a rectangle.

Describe around such a polygon rectangle so that its sides were parallel to the grid lines (coordinate axes). At least one of the vertices of the polygon must be a vertex of a rectangle.

3

Divide the space inside the rectangle in the basic shapes (triangles and squares). Find the area of each and add up all the resulting squares. Subtract the area of the rectangle calculated square inner shapes. So you will find the area of a polygon fast enough.

4

Use one of the following formulas to calculate the area of a regular polygon (angles and sides are equal):

– multiply the number of corners (sides) of the polygon n at two radius r of the inscribed circle and the tangent (π/n);

– multiply (n/2) for two radius R of the circumscribed circle and the sine (2π/n);

– multiply (n/4) for two radius r of the incircle and the cotangent (π/n).

– multiply the number of corners (sides) of the polygon n at two radius r of the inscribed circle and the tangent (π/n);

– multiply (n/2) for two radius R of the circumscribed circle and the sine (2π/n);

– multiply (n/4) for two radius r of the incircle and the cotangent (π/n).

5

Use the following formula, when known side of the triangle:

– multiply the side of the triangle that are adjacent to the corner C, the sine of this angle;

– subtract properiety (p) of the triangle first, one side (p-a), then the other (p-b) and third (p-c). Multiply the values obtained with pauperisation and divide the result by 2.

– multiply the side of the triangle that are adjacent to the corner C, the sine of this angle;

– subtract properiety (p) of the triangle first, one side (p-a), then the other (p-b) and third (p-c). Multiply the values obtained with pauperisation and divide the result by 2.

6

Use to find the area of a trapezoid the formula S = h * ( a + b ) / 2, if we know the height and both bases of the trapezoid.

7

Use a method of calculating square of polygon with the help of palettes. Draw a polygon around the square grid, in which the side of one cell will be equal to one for all vertices of the polygon were located in the nodes.

8

Calculate the area of this figure by the formula of Peak: S = B + G/2 – 1. Here is the number of grid points located inside the polygon, and G is the number of nodes of a square grid located at the border of the polygon.