Finding the perimeter of various Peterson figures. Problems for finding the perimeter and area

Problems for finding area and perimeter

geometric shapes

Compiled by:

teacher primary school

MKOU secondary school №1 named after A.M. Gorky

Frolovo urban district

Kislova Ludmila Borisovna

Frolovo - 2014

I level.

1. The length of the rectangle is 8 dm, the width is 7 dm. Find its area.

2. The length of the side of the square is 6 cm. Find out the area and perimeter of the square.

The difference between a square and a rhombus has to do with the slope of the sides and therefore the alpinism of the formed corners. You already know that in a square, the four corners have the same width, that is, 90 degrees. Thus, the intersection of its sides forms four right angles.

In the rumble, things change a little. We try to understand better, starting with the drawing. If, for example, a were equal to 4, then all sides of our turbo paper would have a length equal to. The angles are equal in pairs. Opposite corners with the same width are called "congruent".

Other important aspect screens are diagonal, that is, segments that stretch between opposite corners. They are perpendicular to each other. In practice, they intersect at the central point of the rhombus and at this point form four right angles. It should also be noted that the diagonals divide the rhombus into four parts, that is, into four triangles the same shape and size.

3. The rectangle has a length of 7 cm, a width of 5 cm. Find out the area and perimeter of the rectangle.

4.Find the perimeter and area of a rectangle with sides 6 cm and 8 cm.

5. The length of the rectangle is 8 dm, the width is 5 dm. Find its area.

6. Calculate the area of a rectangle whose side lengths are 6 mm and 8 mm.

7. The width of the rectangle is 7 dm, and the length is 12 dm. Calculate the area.

How to calculate the perimeter of a rhombus

Now we have all the data and information to calculate the perimeter and area of the rhombus. Calculation of the perimeter of quadrilaterals and flat figures in general, very simple. Just add the measure of all sides. In this case, having a rhombus with four sides of the same length, simply multiply one side by.

In the picture above, we saw that the side measures a, so the formula for the perimeter. The same would be written: sum four times a. If the side of a rhombus measures 5, what is its perimeter? Perimeter formula: so since our a measure is 5, we will have: =.

8. The length of the rectangle is 9 dm, the width is 7 cm. Find its area.

9. The length of the side of the square is 6 cm. Find out the area.

10. Calculate the perimeter of a square with a side of 4 cm.

11. The width of the rectangle is 9 dm, and the length is 6 dm more. Find its area.

12. The length of the rectangle is 5 dm, the width is 4 cm less. Find the P and S of this rectangle.

How to calculate the area of a rhombus

The side of the diamond is 12, calculate the perimeter. Having learned how to calculate the perimeter, let's look at the area, the formula of which is somewhat more complicated. In this operation, the diagonals visible before entering the game. The area is equal to the main diagonal for the minor diagonal, and the whole is divided by two.

So, here are two formulas for calculating the perimeter and area of a rhombus. Calculate the perimeter and area of a diamond with sides 10 and diagonals 12 and 20. Given a side of a rhombus and only one of its diagonals, find the perimeter and area. For this solution, read the second in-depth study below.

13. Draw a rectangle, the length of one side of which is 2 cm, and the length of the other is 3 times longer. Find its perimeter and area.

14. Draw a rectangle, the length of one side of which is 6 cm, and the length of the other is 2 times longer. Find its perimeter and area.

15. Draw a rectangle with a width of 2 cm and a length of 3 cm more. Calculate its perimeter.

Looking at the picture above, according to you, what corresponds to the area of the rhombus? As written earlier, the diagonals divide the rumble into 4 triangles. And therefore it is right to say that the area of a rhombus is equal to the sum of four triangles of regions. Since the triangles are equal to each other, it will be enough to calculate one area of one of the four triangles, and then multiply by.

In fact, by taking one of the triangles drawn in the rhombus, we realize that we know 2 sides by 3: we have the side of the rhombus, which in practice is the hypotenuse, and then one of the two inner sides, which is half the diagonal. The formula for calculating one side of a triangle, knowing the other side and the hypotenuse, is as follows.

16. The side of the square is 3 cm. What is the perimeter?

17. A sheet of paper has square shape. Its side is 10 cm. What is the perimeter?

18. Draw a square with a side of 6 cm. Find its perimeter. The perimeter of a square is 28 cm. What is its side?

19.Window width rectangular shape 4 dm, and the length is 2 times longer. Calculate the area of the window.

That is, Square root the difference between the square of the hypotenuse and the square of the other side. Let's do an exercise. Calculate the diagonal of the rhombus, knowing that the side of the rhombus is 8 and the other diagonal is. From the formula we find the third side of the triangle, which we skip, and then it will be half the diagonal.

And this is the third side that we were missing: 5. To calculate the diagonal of a rhombus, simply multiply by 2 to get 10. With these three data, we can easily find the perimeter and area. Perimeter and Area of other geometric shapes. By following the blue links listed above, you can read the linked pages with all the information about the chosen flat drawing.

20. The width of the rectangle is 4 dm, and the length is 5 times the width. Find the area of the rectangle.

21. The area of a rectangle is 36 cm², its length is 9 cm. What is the width of the rectangle?

II level

1. Draw a rectangle, the length of one side of which is 2 cm, and the length of the other is 4 times longer. Find its perimeter and area.

2. The length of the rectangle is 5 dm, the width is 4 cm less. Find the P and S of this rectangle.

3. Given: a rectangle, a \u003d 8 dm, b - 2 cm less. Find R and S.

4. The length of the rectangle is 12 cm, and its width is 2 cm less. Find the area and perimeter of the rectangle.

5. The sum of the two sides of the square is 12 dm. Find the perimeter and area of the square.

6. Find the length of the rectangle by its width - 8 dm and perimeter - 30 dm.

7. The perimeter of a square is 32 cm. What is its side?

8. The perimeter of the triangle is 21 cm. Put on the length of the third side of this triangle if the lengths of the two sides are 7 cm and 8 cm.

9. The perimeter of the rectangle is 20 cm. The length of its side is 6 cm. Find out the width of the rectangle and draw it.

10. The area of the rectangle is 270 sq. cm, its length is 9 dm. Find the perimeter of this rectangle.

11.Perimeter rectangle is 54 m. Find the area of this rectangle if one of its sides is 18 m.

12. Find the area of a square whose perimeter is 360 mm.

13. The perimeter of the rectangle is 40 cm. One side is 5 cm. What is its area?

14. Draw a square whose perimeter is equal to the perimeter of a rectangle with sides 2 cm and 6 cm.

15. A suburban area of rectangular shape has a length of 20 m and a width of 12 m. How long should a fence be placed around the site?

16. The perimeter of a square is equal to the perimeter of a triangle with sides 6 cm, 3 cm and 7 cm. What is the length of the side of the square?

17. Which figure has an area larger and by how much: a square with a side of 4 cm or a rectangle with sides of 2 cm and 6 cm?

18. The perimeter of a rectangle is 54 m. Find the area of this rectangle if one of its sides is 18 m.

19. The perimeter of a square sandbox is 12 m. Find the area of this sandbox.

20. Write everything possible options length and width of a rectangle if its perimeter is 24 cm.

Internet resources used