Math Exercises & Math Problems: Perimeter and Area of Plane Figures 
Find the perimeter and the area of a square, if we know the length of its diagonal d = 4.2 m.
Find the area of the rectangle ABCD, where the length of the side AB = a = 8.2 cm and the diagonal d = 2a.
Lengths of the sides of a rectangular garden are in the ratio 1 : 2. Line connecting the centers of the adjacent sides of the garden is 20 m long. Calculate the perimeter and the area of the garden.
A rectangular garden has a length of 57 m and a width of 42 m. Calculate of how many m^{2} will decrease the area of a garden, if the ornamental fence with a width of 60 cm will be planted inside its perimeter.
A perimeter of a parallelogram is 2.8 meters. The length of one of its sides is equal to oneseventh of the entire perimeter. Find lengths of the sides of the parallelogram.
One of the internal angles of the rhombus is 120° and the shorter diagonal is 3.4 meters long. Find the perimeter of the rhombus.
Find a length of the diagonal AC of the rhombus ABCD if its perimeter P = 112 dm and the second diagonal BD has a length of 36 dm.
In the isosceles trapezoid ABCD we know: ABCD, CD = c = 8 cm, height h = 7 cm, ∠CAB = 35°. Find the area of the trapezoid.
A trapezoid ABCD has the bases length of a = 120 mm, c = 86 mm and the area A = 2,575 mm^{2}. Find the height of the trapezoid.
Consider the isosceles trapezoid PQRS. The bases are PQ = 120 mm, RS = 62 mm and the arm s = 48 mm. Find the height of the trapezoid, diagonal length and the area of the trapezoid.
A land of a rightangled trapezoid shape has the bases lengths of 92 m and 76 m and the vertical arm is 6.3 m long. Find the land area and the length of a fencing needed to fence the land.
A perimeter of an isosceles triangle is 474 m. The base of the triangle is by 48 m longer than the arm. Find the length of the sides and the area of the triangle.
A rightangled triangle ABC has the legs a = 5 cm, b = 8 cm. A triangle A'B'C' is similar to the triangle ABC and it is 2.5 times smaller. Calculate what percentage of the area of the triangle ABC takes the area of the triangle A'B'C'.
A rightangled isosceles triangle has the area of 32 cm^{2}. What is its perimeter ?
An equilateral triangle has the perimeter of 36 dm. What is its area ?
A triangle ABC has side lengths a = 14 cm, b = 20 cm, c = 7.5 cm. Find the size of the internal angles and the area of the triangle.
Find the perimeter, the area and the size of remaining angles of a triangle ABC, when: a = 8.4, β = 105°35' and median of side a is m_{a} = 12.5.
Find the lenght of all sides and the size of all internal angles of the triangle ABC, if we know: A = 501.9; α = 15°28' and β = 45°.
A parallelogram ABCD has the area of 40 cm^{2}, AB = 8.5 cm and BC = 5.65 cm. Find the length of its diagonals.
Find the area of a regular hexagon, if we know the radius of its inscribed circle ρ = 4 cm.
In the regular hexagon ABCDEF the diagonal AC has the length of 12 cm. Find the length of the side of the hexagon ABCDEF and determine its area.
Find the perimeter of a circle if its area is 706.5 cm^{2}.
Find the area of a circle if its perimeter is 94.2 dm.
A square on the picture has 8 cm long side. Find the area of the colored part of a circle.
On the picture two and another two semicircles are identical. The radius of one semicircle is twice as large as the radius of the other semicircle. Find the area of the colored pattern if AB = 12 cm.
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