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?

Correct answer:

S =  47 cm²

Step-by-step explanation:

$$\begin{gathered} a=16\text{ cm } \\ b=4\text{ cm } \\ {S}_0=a\cdot b=16\cdot 4=64{\text{cm}}^2 \\ x+y=a \\ {x}^2=y^2+b^2 \\ x+y=16 \\ {y}^2=x^2+4^2=7.5^2+4^2=16 \\ x=15\mathrm{/}2={\displaystyle \frac{15}{2}}=7.5\text{ cm } \\ y=17\mathrm{/}2={\displaystyle \frac{17}{2}}=8.5\text{ cm } \\ {S}_1={\displaystyle \frac{b\cdot x}{2}}={\displaystyle \frac{4\cdot 7.5}{2}}=15{\text{cm}}^2 \\ {S}_2=x\cdot b=7.5\cdot 4=30{\text{cm}}^2 \\ {S}_3=(y-x)\cdot b\mathrm{/}2=(8.5-7.5)\cdot 4\mathrm{/}2=2{\text{cm}}^2 \\ S=S_1+S_2+S_3=15+30+2=47{\text{cm}}^2 \end{gathered}$$

Try another example

Related math problems and questions:

• Rectangle JANO
  The rectangle has side lengths | JA | = 16cm and | AN | = 12cm. Point S is the center of the JO side and point T is the center of the JA side. Calculate the perimeter of the pentagon in cm.
• MO Z8–I–6 2018
  In the KLMN trapeze, KL has a 40 cm base and an MN of 16 cm. Point P lies on the KL line so that the NP segment divides the trapezoid into two parts with the same area. Find the length of the KP line.
• 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.
• A rectangle 8
  A rectangle measuring 6 cm and 4 cm is enlarged by the ratio 3:1. What is the area of the enlarged rectangle?
• Colored paper
  Can a 4 cm, 3 cm and 2 cm block be glued with a colored quarter of paper measuring 7 cm and 8 cm?
• 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?
• Octagonal mat
  Octagonal mat formed from a square plate with a side of 40 cm so that every corner cut the isosceles triangle with leg 3.6 cm. What is the content area of one mat?
• The plan
  Students have collected 48 kg of paper which is 16% of the plan. How many kg of paper still have to collect to fulfill the plan?
• After 16 years
  After 16 years will Dana be five times older as she was four years ago. After how many years will Dana celebrate her 16th birthday?
• Pentagon
  Calculate the area of a regular pentagon, which diagonal is u=16.
• Glass of juice
  Glass of juice shaped cylinder 16 cm height and base diameter of 7 cm is filled with juice so that the level is 4 cm below the rim of the glass. Determine the maximum angle of the cup can be tilted and juice don't overflow.
• Kite
  John a kite, which is diamond-shaped. Its diagonals are 60 cm long and 90 cm long. Calculate: a) the diamond side b) how much paper John needs to make a kite if he needs a paper on both sides and needs 5% of the paper for bending.
• Brackets
  Place one pair of brackets in expression 20-16 + 10 - 4 - 2 so that the result will be 0.
• Intersections
  How many intersections have circles with radius 16 mm and 15 mm, if the distance of their centers is 16 mm.
• Quadrilateral eq3
  Three sides of a quadrilateral are equal to the foreside which is 16 cm long. What is the length of the one with equal sides if the perimeter is 58 cm?
• Enlarged rectangle
  The rectangle with dimensions of 8 cm and 12 cm is enlarged in a ratio of 5:4. What are the circumference and the area of the enlarged rectangle?
• 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?