Problems of area of plane shapes
- Diagonal to area
Calculate the area of a rectangle in which the length of the diagonal is 10 cm.
- Map scale
The rectangular plot has in a scale of 1: 10000 area 3 cm2 on the map. What content does this plot have on a 1:5000 scale map?
- Coordinate axes
Determine the area of the triangle given by line -7x+7y+63=0 and coordinate axes x and y.
- Trapezoid - intersection of diagonals
In the ABCD trapezoid is AB = 8 cm long, trapezium height 6 cm, and distance of diagonals intersection from AB is 4 cm. Calculate trapezoid area.
- Annual rainfall
The average annual rainfall is 686 mm. How many liters will fall on the 1-hectare field?
- Rectangle area
The length of a rectangle of x units is increased by 10% and its width of y units is increased by 15%. What is the ratio of the area of the old rectangle to the area if the new rectangle?
- Pravoúhly trojúhelník
Určete obsah pravoúhlého trojúhelníku, jehož délky stran tvoří po sobě jdoucí členy aritmetické posloupnosti a poloměr kružnice opsané tomuto trojúhelníku je 5 cm.
Area of square garden is 6/7 of triangle garden with sides 96 m, 60 m and 60 m. How many meters of fencing need to fence a square garden?
- Trapezoid MO
The rectangular trapezoid ABCD with right angle at point B, |AC| = 12, |CD| = 8, diagonals are perpendicular to each other. Calculate the perimeter and area of the trapezoid.
- Right Δ
Right triangle has length of one leg 68 cm and length of the hypotenuse 85 cm. Calculate the height of the triangle.
- Triangle SAS
Calculate area and perimeter of the triangle, if the two sides are 19 cm and 80 cm long and angle them clamped is 90°.
- Tetrahedral pyramid
What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=23 and height v=8?
Points A[1,5] and B[-4,-5] are adjacent vertices of the square ABCD. Calculate area of the square ABCD.
Swimming pool is long 110 m and 30 m wide. The plan of the city is shown as a rectangle with area 13200 cm2. What scale is the city plan?
- Regular 5-gon
Calculate area of the regular pentagon with side 11 cm.
Calculate the perimeter and area of rhombus whose diagonals are 26 cm and 42 cm long.
- Right triangle Alef
The perimeter of a right triangle is 132 cm, the hypotenuse is 55 cm long. Determine the lengths of the legs.
The cube has area of base 400 mm2. Calculate the edge length, volume and area of its surface.
In rectangle with sides 10 and 9 mark the diagonal. What is the probability that a randomly selected point within the rectangle is closer to the diagonal than to any side of the rectangle?
- Area of RT
Calculate the area of a right triangle which hypotenuse has length 15 and one hypotenuse segment has lenght 11.