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 cm² and the rectangle MLGH area is 28 cm². Find the area of the IFJD rectangle.

Correct answer:

S =  418 cm²

Step-by-step explanation:

$$\begin{gathered} S_1=12{\text{cm}}^2 \\ {S}_2=63-S_1=63-12=51{\text{cm}}^2 \\ {S}_3=28-S_1=28-12=16{\text{cm}}^2 \\ a=\mathrm{\mid }MB\mathrm{\mid }=random \\ a=5\text{ cm } \\ {S}_1=a\cdot b \\ {S}_2=a\cdot c \\ {S}_3=b\cdot d \\ b=S_1\mathrm{/}a=12\mathrm{/}5={\displaystyle \frac{12}{5}}=2.4\text{ cm } \\ c=S_2\mathrm{/}a=51\mathrm{/}5={\displaystyle \frac{51}{5}}=10.2\text{ cm } \\ d=S_3\mathrm{/}b=16\mathrm{/}2.4={\displaystyle \frac{20}{3}}\doteq 6.6667\text{ cm } \\ x=d+a+d=6.6667+5+6.6667={\displaystyle \frac{55}{3}}\doteq 18.3333\text{ cm } \\ y=c+b+c=10.2+2.4+10.2={\displaystyle \frac{114}{5}}=22.8\text{ cm } \\ S=x\cdot y=18.3333\cdot 22.8=418{\text{cm}}^2 \end{gathered}$$

Try another example

Related math problems and questions:

• Trapezoid MO-5-Z8
  ABCD is a trapezoid that lime segment CE is divided into a triangle and parallelogram, as shown. Point F is the midpoint of CE, DF line passes through the center of the segment BE, and the area of the triangle CDE is 3 cm². Determine the area of the trape
• Square grid
  Square grid consists of a square with sides of length 1 cm. Draw in it at least three different patterns such that each had a content of 6 cm² and circumference 12 cm and that their sides is in square grid.
• Rectangle - sides 3
  If in the rectangle ABCD we enlarge the side a by 5 cm and decrease the side b by 2 cm, the rectangle area will be reduced by 5 cm². When we decrease the length of the side a by 4 cm and and at the same time we increase the length of side b by 3 cm we inc
• Hexagon - MO
  The picture shows the ABCD square, the EFGD square and the HIJD rectangle. Points J and G lie on the side CD and is true |DJ|
• MO-Z5-3-66 tiles
  The picture shows a square tiles with side 10 dm which is composed of four identical small rectangles and squares. Circumference of small square is five times smaller than the circumference of the entire tile. Determine the dimensions of the rectangle.
• 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
• 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)
• Isosceles - isosceles
  It is given a triangle ABC with sides /AB/ = 3 cm /BC/ = 10 cm, and the angle ABC = 120°. Draw all points X such that true that BCX triangle is an isosceles and triangle ABX is isosceles with the base AB.
• Square into three rectangles
  Divide the square with a side length of 12 cm into three rectangles with have the same circumference so that these circumferences are as small as possible.
• Parallelogram ABCD
  The area of parallelogram ABCD is 440 cm². Points M and N are the midpoints of the sides AB and BC. What is the area of a quadrilateral MBND?
• Two rectangles 2
  A square of area 36 cm² is cut out to make two rectangles. A and B The area of area A to area B is 2 : 1 Find the dimensions of rectangles A and B.
• MO - triangles
  On the AB and AC sides of the triangle ABC lies successive points E and F, on segment EF lie point D. The EF and BC lines are parallel and is true this ratio FD:DE = AE:EB = 2:1. The area of ABC triangle is 27 hectares and line segments EF, AD, and DB seg
• Internal angles
  The ABCD is an isosceles trapezoid, which holds: |AB| = 2 |BC| = 2 |CD| = 2 |DA|: On its side BC is a K point such that |BK| = 2 |KC|, on its side CD is the point L such that |CL| = 2 |LD|, and on its side DA the point M is such that | DM | = 2 |MA|. Dete
• Rectangles
  How many different rectangles can be made from 60 square tiles of 1 m square? Find the dimensions of these rectangles.
• 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.
• Rectangles
  How many different rectangles with sides integers (in mm) have a circumference exactly 1000 cm? (a rectangle with sides of 50cm and 450cm is considered to be the same as a rectangle with sides of 450cm and 50cm)
• MO 2016 Numerical axis
  Cat's school use a special numerical axis. The distance between the numbers 1 and 2 is 1 cm, the distance between the numbers 2 and 3 is 3 cm, between the numbers 3 and 4 is 5 cm and so on, the distance between the next pair of natural numbers is always i