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 result:

S =  47 cm²

Solution:

$$\begin{gathered} a=16\text{ cm } \\ b=4\text{ cm } \\ {S}_0=a\cdot b=16\cdot 4=64{\text{cm}}^2 \\ x+y=a \\ {x}^2=y^2+b^2 \\ x+y=16 \\ {y}^2=x^2+4^2=7.5^2+4^2=18 \\ x=15\mathrm{/}2={\displaystyle \frac{15}{2}}=7.5\text{ cm } \\ y=17\mathrm{/}2={\displaystyle \frac{17}{2}}=8.5\text{ cm } \\ {S}_1={\displaystyle \frac{b\cdot x}{2}}={\displaystyle \frac{4\cdot 7.5}{2}}=15{\text{cm}}^2 \\ {S}_2=x\cdot b=7.5\cdot 4=30{\text{cm}}^2 \\ {S}_3=(y-x)\cdot b\mathrm{/}2=(8.5-7.5)\cdot 4\mathrm{/}2=2{\text{cm}}^2 \\ S=S_1+S_2+S_3=15+30+2=47{\text{cm}}^2 \end{gathered}$$

Try another example

Showing 0 comments:

Next similar math problems:

• 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?
• 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.
• 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 paper on both sides and needs 5% of the paper for bending.
• Pentagon
  Calculate the area of a regular pentagon, which diagonal is u=17.
• Stairs
  Between adjacent levels are 15 stairs. If step will be 1.2 cm lower there would be 16 stairs. What is the stair height?
• Pentagon
  Calculate the length of side, circumference and area of a regular pentagon, which is inscribed in a circle with radius r = 6 cm.
• 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
• Paper box
  Calculate the consumption of paper on the box-shaped quadrangular prism with rhombic footstall, base edge a=6 cm and the adjacent base edges forms an angle alpha = 60 °. Box height is 10 cm. How many m² of the paper consumed 100 such boxes?
• 6 regular polygon
  It is given 6 side regular polygon whose side is 5 cm. Calculate its content area. Compare how many more cm² (square centimeters) has a circle in which is inscribed the 6-gon.
• Paper squares
  The paper rectangle measuring 69 cm and 46 cm should be cut into as many squares as possible. Calculate the lengths of squares and their number.
• Regular 5-gon
  Calculate the area of the regular pentagon with side 7 cm.
• 2d shape
  Calculate the content of a shape in which an arbitrary point is not more than 3 cm from the segment AB. The length of the segment AB is 5 cm.
• Find the
  Find the content of a regular 12 sided polygon, if its side a = 12 cm.
• Two rectangles
  I cut out two rectangles with 54 cm², 90 cm². Their sides are expressed in whole centimeters. If I put these rectangles together I get a rectangle with an area of 144 cm². What dimensions can this large rectangle have? Write all options. Explain your calc
• The circumference
  The circumference and width of the rectangle are in a ratio of 5: 1. its area is 216cm2. What is its length?
• Do you solve this?
  Determine area S of rectangle and length of its sides if its perimeter is 102 cm.
• Parallelogram
  Calculate area of the parallelogram ABCD as shown if |AB| = 19 cm, |BC| = 18 cm and angle BAD = 90°