Examples of area of plane shapes

Area is the quantity that expresses the extent of a two-dimensional shape. The area can be understood as the amount of paint necessary to cover the surface with a single coat. The area of a shape can be measured by comparing the shape to squares of a fixed size 1 m^2 or 1 cm^2 etc. Every unit of length has a corresponding unit of area. Areas can be measured in square metres (m^2), square centimetres (cm^2), square millimetres (mm^2), square kilometres (km^2), square feet (ft^2), square yards (yd^2), square miles (mi^2), and so forth.

Number of problems found: 745

Present
Gift box has a rectangular shape with dimensions of 8×8×3 cm. Miloslav wants to cover with square paper with sides of 18 cm. How much paper left him?
Square garden
On the plan with a scale of 1:1500 is drawn as a square garden with area 81 cm². How many meters is long garden fence? Determine the actual acreage gardens.
Trapezoid IV
In a trapezoid ABCD (AB||CD) is |AB| = 15cm |CD| = 7 cm, |AC| = 12 cm, AC is perpendicular to BC. What area has a trapezoid ABCD?
Tailor
Tailor has an estimated 11 meters of 80 cm wide fabric. He will shape wholly 7 rectangles measuring 80 x 150 cm and nothing fabric does not remain. How many fabric he have?
Two annuluses
The area of the annular circle formed by two circles with a common center is 100 cm². The radius of the outer circle is equal to twice the radius of the inner circle. Determine the outside circle radius in centimeters.
Ratio - rectangle
The rectangle has dimensions 6 cm and 9 cm. How many times increases area and its perimeter, when its dimensions increase in the ratio 5:3?
Circular segment
Calculate the area S of the circular segment and the length of the circular arc l. The height of the circular segment is 2 cm and the angle α = 60°. Help formula: S = 1/2 r2. (Β-sinβ)
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.
Two squares
Two squares whose sides are in the ratio 5:2 have a sum of its perimeters 73 cm. Calculate the sum of the area of these two squares.
Two 2D shapes
Decide which shapes have more area: (a) a square of 8cm side; or (b) two rectangles with sides 5cm and 15cm? Write result as 1 or 2 (rectangles)
Regular quadrangular pyramid
How many square meters are needed to cover the tower the shape of a regular quadrangular pyramid base edge 10 meters, if the deviation lateral edges from the base plane are 68 °? Calculate coverage of waste by 10%.
Floor
The floor area of the room is 31 m² and has a width of 4.3 m. How many centimeters of circumference measured floor on the map at the scale 1:75?
KLMN trapezoid
The KLMN trapezoid has bases KL 40cm and MN 16cm. On the KL base is point P. The segment NP divides the trapezoid into units with the same area. What is the distance of point P from point K?
Observatory
Observatory dome has the shape of a hemisphere with a diameter d = 16 m. Calculate the surface.
Rectangular field
A rectangular field has a diagonal of length 169m. If the length and width are in the ratio 12:5. Find the dimensions of the field, the perimeter of the field and the area of the field.
Octagonal tank
The tank has the shape of a regular octagonal prism without an upper base. The base edge has a = 3m, the side edge b = 6m. How much metal sheet is needed to build the tank? Do not think about losses or sheet thickness.
Orange and tangerine trees
Brad's father asked an engineer to survey the field behind their house. He wanted to plant some orange and tangerine trees there. According to the survey, the field is thirty-two feet long and six yards wide. What is the area of the field in sq feet?
Trapezoid
Area of trapezoid is 135 cm². Sides a, c and height h are in a ratio 6:4:3. How long are a,c and h? Make calculation...
Church roof
The roof of the church tower has the shape of a regular tetrahedral pyramid with base edge length 5.4 meters and a height 5 m. It was found that needs to be corrected 27% covering of the roof area. What amount of material will be required?
Windows
Calculate the area of masonry to build wall with dimensions of 9 m × 4 m with 4 windows of size 64 cm × 64 cm.

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