# Examples of area of plane shapes

1. Perimeter to area
Calculate the area of a circle with the perimeter 15 meters.
2. Diagonals of diamond
Find the area and circumference of the diamond ABCD with 15m and 11m diagonals.
3. Trapezoid - central median
The central median divides the trapezoid into two smaller trapezoids. Determines the ratio of their contents.
4. Rectangular trapezoid
The rectangular trapezoid ABCD is: /AB/ = /BC/ = /AC/. The length of the median is 6 cm. Calculate the circumference and area of a trapezoid.
5. Diameter to area
Find the area of a circle whose diameter is 26cm.
6. Trapezium
The lengths of a parallel sides of a trapezium are (2x+3) and (x+8) and the distance between them is (x+4). if the area of the trapezium is 590 , find the value of x.
7. Triangle ABC v2
Area of the triangle is 12 cm square. Angle ACB = 30º , AC = (x + 2) cm, BC = x cm. Calculate the value of x.
8. Pentagon
Calculate the length of side, circumference and area of a regular pentagon, which is inscribed in a circle with radius r = 6 cm.
9. 2d shape
Calculate the content of a shape in which an arbitrary point is not more than 3 cm from the segment AB. The length of the segment AB is 5 cm.
10. Rectangle 3-4-5
The sides of the rectangle are in a ratio of 3:4. The length of the rectangle diagonal is 20 cm. Calculate the content of the rectangle.
11. Perimeter from area
What is the perimeter of the square if its content is 64 cm2?
12. Hamster cage
Ryan keeps his hamster cage on his dresser. The area of the top of Ryan's dresser is 1 2\3 as large as the area of the bottom of his hamster cage. The area of the dresser top is 960 square inches. How many square inches of his dresser top are not covered
13. Cuboid and eq2
Calculate the volume of cuboid with square base and height 6 cm if the surface area is 48 cm2.
14. Diagonals of a rhombus
One of the diagonals of a rhombus is twice as the other. If the sum of the lengths of the diagonals is 24, find the area of the rhombus.
15. Right triangle eq2
Hypotenuse of a right triangle is 9 cm longer than one leg and 8 cm longer than the second leg. Determine the circumference and area of a triangle.
16. Rhombus and diagonals
The a rhombus area is 150 cm2 and the ratio of the diagonals is 3:4. Calculate the length of its height.
17. Trapezium 2
Trapezium has an area of 24 square cms. How many different trapeziums can be formed ?
18. Square vs rectangle
Square and rectangle have the same area contents. The length of the rectangle is 9 greater and width 6 less than side of the square. Calculate the side of a square.
19. Trapezoid MO-5-Z8
ABCD is a trapezoid that lime segment CE divided into a triangle and parallelogram as shown. Point F is the midpoint of CE, DF line passes through the center of the segment BE and the area of the triangle CDE is 3 cm2. Determine the area of the trapezoid
20. Hypotenuse
Calculate the length of the hypotenuse of a right triangle if the length of one leg is 4 cm and its content area is 16 square centimeters.

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