# Irregular pentagon

A rectangle-shaped, 16 x 4 cm strip of paper is folded lengthwise so that the lower right corner is applied to the upper left corner. What area does the pentagon have?

Result

S =  47 cm2

#### Solution:

$a=16 \ \text{cm} \ \\ b=4 \ \text{cm} \ \\ S_{0}=a \cdot \ b=16 \cdot \ 4=64 \ \text{cm}^2 \ \\ \ \\ x+y=a \ \\ x^2=y^2+b^2 \ \\ \ \\ x+y=16 \ \\ y^2=x^2+4^2=7.5^2+4^2=18 \ \\ \ \\ x=15/2=\dfrac{ 15 }{ 2 }=7.5 \ \text{cm} \ \\ y=17/2=\dfrac{ 17 }{ 2 }=8.5 \ \text{cm} \ \\ \ \\ S_{1}=\dfrac{ b \cdot \ x }{ 2 }=\dfrac{ 4 \cdot \ 7.5 }{ 2 }=15 \ \text{cm}^2 \ \\ S_{2}=x \cdot \ b=7.5 \cdot \ 4=30 \ \text{cm}^2 \ \\ S_{3}=(y-x) \cdot \ b/2=(8.5-7.5) \cdot \ 4/2=2 \ \text{cm}^2 \ \\ \ \\ S=S_{1}+S_{2}+S_{3}=15+30+2=47 \ \text{cm}^2$

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Be the first to comment!

## Next similar math problems:

1. Tiles path
A rectangular park measures 24mX18m. A path 2.4m wide is constructed all around it. Find the cost of paving the path with cement tiles of size 60cm X 40cm at the rate of \$5.60 per tile ?
2. Window
Peter demolish box hole in the wall for window frame 147×51 cm. When they came masters fitted frame and window will be found that glass is 13.3 cm from the hole in each direction. Calculate how much percent less light enters the window than hole?
3. Bathroom 2
A bathroom is 2.4 meters long and 1.8 meters wide. How many square tiles 1 dm on each side are to be used to cover it?
4. Lawns
Before a sports hall are two equally large rectangular lawns, each measuring 40 m and 12 m. Maintenance of 10m² lawn cost 45 CZK yearly. On each lawn is circular flowerbed with a diameter 8 meters. How much money is needed each year to take on lawn care?
5. Rectangular field
One dimension of the rectangular field is 56 m greater than second dimension. If each side of the rectangle increases by 10 m, increases the surface field is 1480 m2 . Determine dimencions of the field.
6. The carpet
How many meters of carpet 90 cm wide need to cover floor room which has a rectangular shape with a lengths 4.8 m and 2.4 m if the number of pieces on the carpet is needed to be lowest?
7. MO8-Z8-I-5 2017
Identical rectangles ABCD and EFGH are positioned such that their sides are parallel to the same. The points I, J, K, L, M and N are the intersections of the extended sides, as shown. The area of the BNHM rectangle is 12 cm2, the rectangle MBCK area is 63.
8. Rectangle A2dim
Calculate the side of the rectangle, if you know that its area is of 2590 m2 and one side is 74 m.
9. Playground
Fencing square playground cost € 464; 1 meter cost € 19. What is the area of the playground?
10. Drawer
The rectangular face of a drawer has a perimeter of 108 cm and a width of 18cm. Find the length and the area of the rectangular face of the drawer.
11. Pipe cross section
The pipe has an outside diameter 1100 mm and the pipe wall is 100 mm thick. Calculate the cross section of this pipe.
12. Rhombus
PQRS is a rhombus. Given that PQ=3 cm & height of rhombus is given 2 cm. Calculate its area.
13. Trapezium 2
Trapezium has an area of 24 square cms. How many different trapeziums can be formed ?
14. Trapezium
The area of trapezium is 35cm2 find its altitude if the bases are 6cm and 8cm.
15. Garden
The garden around the new majer is divided as follows: 35% vegetable, 30% fruit orchards, 10% flowers and the remaining 120 m2 are lawns. What is the total area of the garden?
16. Factory
In the factory workers work in three shifts. In the first inning operates half of all employees in the second inning and a third in the third inning 200 employees. How many employees work at the factory?
17. Down syndrome
Down syndrome is one of the serious diseases caused by a gene mutation. Down syndrome occurs in approximately every 550-born child. Express the incidence of Down's syndrome in newborns at per mille.