Advice 1: How to find the area knowing the perimeter

Area and perimeter shapes are the main geometric parameters. Their presence and description with the given values is a significant part of the learning process. In a General sense, the perimeter is the length of all borders of the shape. For a rectangle it is the sum of the lengths of its sides. And the area represents the entire inner part of the figure, measured in certain units. According to the properties of figures and the formulas of area and perimeterand to find correlation between these parameters and shapes to Express one value from another. To find the area of a rectangle with a known perimeterof ω must also know one side of it.
How to find the area knowing the perimeter
Instruction
1
Write the known parameters of the rectangular figure. In addition to the perimeterand to find the area needs to be known is another value either side of the rectangle.
How to find the area, knowing <b>perimeter</b>
2
According to the formula, the perimeter of the rectangle is, as the sum of all its sides. Because in a rectangle opposite sides are equal, we can write the formula for the perimeter: P = (d+c)*2, where d and c are the adjacent sides of shapes.
3
The area of rectangular shapes is determined by the product of its two adjacent sides: S = d*c. Thus, knowing one side, you can easily find the area of the shape.
4
Substitute in the formula for the perimeterand the known values: one of the sides and the perimeter. Express from the resulting equations the second unknown side and calculate it. Substitute the value obtained into the formula area. Calculate the value of the S - square shape.
How to find the area, knowing <b>perimeter</b>

Advice 2 : How to find the sides of the rectangle

A special case of a parallelogram - rectangle – only known in Euclidean geometry. Have a rectangle all the angles are equal, and each of them individually is 90 degrees. On the basis of private properties of the rectangleand from the properties of the parallelogram of the parallel opposite sides can find a hand figure by the given diagonals and angle from their intersection. Calculating sides of a rectangle based on additional constructions and apply the properties of the resultant shapes.
How to find the sides of the rectangle
Instruction
1
Draw a rectangle EFGH. Record the known data: the diagonal of the rectangle EG, and the angle α, obtained from the intersection of the two equal diagonals FH and EG. Build the figure and mark the diagonal between them the angle α.
How to find <b>hand</b> <strong>rectangle</strong>
2
The letter And mark the point of intersection of the diagonals. Consider the constructions formed by the triangle EFА. According to the property of the rectangle, its diagonals are equal and are bisected by the intersection point A. Calculate the values of FA and EA. Since the triangle is isosceles EFА and his side of EA and FA are equal and accordingly equal to half the diagonal EG.
3
Next, calculate the first side EF of the rectangle. This is the third unknown side of the considered triangle EFА. According to the theorem of the cosines of the appropriate formula, find the side EF. To do this, substitute in the formula for cosines of the previously obtained values of FA equal to the sides EA and the cosine of the known angle α between them. Calculate and record the obtained value of EF.
How to find <b>hand</b> <strong>rectangle</strong>
4
Find the second side of the rectangle FG. For this we consider another triangle EFG. It is rectangular, where the hypotenuse BC and the side EF. According to the Pythagorean theorem, find the second leg FG with the applicable formula.
How to find <b>hand</b> <strong>rectangle</strong>
5
In accordance with the properties of the rectangle, its opposite edges are equal. Thus, the side GH is equal to the side EF, and = FG. Write in the answer all the computed sides of the rectangle.
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