MO Z9–I–2 - 2017

In the VODY trapezoid, VO is a longer base and the diagonal intersection K divides the VD line in a 3:2 ratio. The area of the KOV triangle is 13.5 cm². Find the area of the entire trapezoid.

Correct result:

S =  37.5 cm²

Solution:

$$\begin{gathered} S_1=13.5{\text{cm}}^2 \\ {k}_2=(2\mathrm{/}3{)}^2={\displaystyle \frac{4}{9}}\doteq 0.4444 \\ {S}_2=k_2\cdot S_1=0.4444\cdot 13.5=6{\text{cm}}^2 \\ {k}_3=(2+3)\mathrm{/}3={\displaystyle \frac{5}{3}}\doteq 1.6667 \\ {S}_3=k_3\cdot S_1-S_1=1.6667\cdot 13.5-13.5=9{\text{cm}}^2 \\ {k}_4=(2+3)\mathrm{/}2={\displaystyle \frac{5}{2}}=2.5 \\ {S}_4=k_4\cdot S_2-S_2=2.5\cdot 6-6=9{\text{cm}}^2 \\ S=S_1+S_2+S_3+S_4=13.5+6+9+9={\displaystyle \frac{75}{2}}={\displaystyle \frac{75}{2}}{\text{cm}}^2=37.5{\text{cm}}^2 \end{gathered}$$

Try another example

Showing 0 comments:

Next similar math problems:

• Isosceles trapezoid
  In an isosceles trapezoid KLMN intersection of the diagonals is marked by the letter S. Calculate the area of trapezoid if /KS/: /SM/ = 2:1 and a triangle KSN is 14 cm².
• Trapezoid - intersection of diagonals
  In the ABCD trapezoid is AB = 8 cm long, trapezium height 6 cm, and distance of diagonals intersection from AB is 4 cm. Calculate the trapezoid area.
• Diagonal intersect
  isosceles trapezoid ABCD with length bases | AB | = 6 cm, CD | = 4 cm is divided into 4 triangles by the diagonals intersecting at point S. How much of the area of the trapezoid are ABS and CDS triangles?
• Trapezoid - diagonal
  A trapezoid has a length of diagonal AC crossed with diagonal BD in the ratio 2:1. The triangle created by points A, cross point of diagonals S and point D has area 164 cm². What is the area of the trapezoid?
• Trapezium diagonals
  It is given trapezium ABCD with bases | AB | = 12 cm, |CD| = 8 cm. Point S is the intersection of the diagonals for which |AS| is 6 cm long. Calculate the length of the full diagonal AC.
• 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?
• Rectangular triangles
  The lengths of corresponding sides of two rectangular triangles are in the ratio 2:5. At what ratio are medians relevant to hypotenuse these right triangles? At what ratio are the contents of these triangles? Smaller rectangular triangle has legs 6 and 8
• Trapezoid thirds
  The ABCD trapezoid with the parallel sides of the AB and the CD and the E point of the AB side. The segment DE divides the trapezoid into two parts with the same area. Find the length of the AE line segment.
• 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.
• Rectangular trapezoid
  The ABCD rectangular trapezoid with the AB and CD bases is divided by the diagonal AC into two equilateral rectangular triangles. The length of the diagonal AC is 62cm. Calculate trapezium area in cm square and calculate how many differs perimeters of the
• Sides od triangle
  Sides of the triangle ABC has length 4 cm, 5 cm and 7 cm. Construct triangle A'B'C' that are similar to triangle ABC which has a circumference of 12 cm.
• Sides ratio
  Calculate the circumference of a triangle with area 84 cm² if a:b:c = 10:17:21
• Diagonals at right angle
  In the trapezoid ABCD, this is given: AB=12cm CD=4cm And diagonals crossed under a right angle. What is the area of this trapezoid ABCD?
• Area of iso-trap
  Find the area of an isosceles trapezoid if the lengths of its bases are 16 cm and 30 cm, and the diagonals are perpendicular to each other.
• Isosceles trapezoid
  Calculate the content of an isosceles trapezoid whose bases are at ratio 5:3, the arm is 6cm long and it is 4cm high.
• 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
• Similarity coefficient
  The ratio of similarity of two equilateral triangles is 3.5 (ie 7:2). The length of the side of smaller triangle is 2.4 cm. Calculate the perimeter and area of ​​the larger triangle.