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 trapezoid ABCD.

Correct result:

S =  12 cm²

Solution:

$$\begin{gathered} \mathrm{\mid }EX\mathrm{\mid }=\mathrm{\mid }XB\mathrm{\mid } \\ S(CDE)=S(AED)=3 \\ S(FCD)=S(FDE)=3\mathrm{/}2=1.5 \\ S(EFX)=S(FCD)=1.5 \\ S(AEDC)=2\cdot 3=6 \\ S(XBCD)=S(AEDC)=2\cdot 3=6 \\ S=S(AEDC)+S(XBCD)-S(FCD)+S(EFX) \\ S=6+6-1.5+1.5=12{\text{cm}}^2 \end{gathered}$$

Try another example

Showing 1 comment:

Math student

The answer is 12 cm²

3 years ago  Like

Next similar math problems:

• Diamond area from diagonals
  In the diamond ABCD is AB = 4 dm and the length of the diagonal is 6.4 dm long. What is the area of the diamond?
• Garden exchange
  The garden has the shape of a rectangular trapezoid, the bases of which have dimensions of 60 m and 30 m and a vertical arm of 40 m. The owner exchanged this garden for a parallelogram, the area of which is 7/9 of the area of a trapezoidal garden. What is
• Children playground
  The playground has the shape of a trapezoid, the parallel sides have a length of 36 m and 21 m, the remaining two sides are 14 m long and 16 m long. Determine the size of the inner trapezoid angles.
• Parallelogram
  Rhomboid (parallelogram) has a longer side of 50 cm long. The size of its one height is four times the size of its second height. Calculate the length of the shorter side of this rhomboid in the centimeters.
• Parallelogram perimeter
  The ABC triangle with sides a = 5cm, b = 3cm, c = 40mm has the center of the sides of the K,L,M. How many cm have the KBLM parallelogram perimeter?
• Parallelogram +ľ
  | AB | = 76cm, | BC | = 44cm, angle BAD = 30 °. Find the area of the parallelogram.
• Quadrilateral 2
  Show that the quadrilateral with vertices P1(0,1), P2(4,2) P3(3,6) P4(-5,4) has two right triangles.
• Parallelogram
  Calculate the missing side of a parallelogram, if you know the perimeter o and one side: a) o = 7.2 cm; b = 1.8 cm b) o = 5.4 cm; a = 1.9 cm
• Midpoints
  Triangle ABC with sides a = 5 cm, b = 3 cm, c = 40mm has a midpoint of K, L, M. How many centimeters is long perimeter of parallelogram KBLM?
• Parallelogram
  In the parallelogram we know one internal angle 67°33`. Calculate the other internal angles.
• Rectangle - parallelogram
  It is given a rectangle that is circumscribed by a circle with a radius of 5 cm. The short side of the rectangle measures 6 cm. Calculate the perimeter of a parallelogram ABCD whose vertices are the midpoints of the sides of the rectangle.
• Prism
  The volume of tetrahedral prism is 2.43 m³. Base of prism is a parallelogram in which a side 2,5dm and height ha = 18cm. Calculate the height of the prism.
• Colour - billboard
  Shelftalker has the shape of a parallelogram. Its length is 4.9 m and the corresponding height is 3.5 meters. Calculate how much (kg) paint must purchase to redecoration if 1 kg cover 4 m² of shelftalker surface.
• The farmer field
  The field has paralleogram shape with dimensions side a = 80 m and height 296 m. Two and two sides is at angle 80°. Calculate acreage of field in hectares.
• Parallelogram
  The parallelogram has sides lengths in the ratio 3: 4 and perimeter 2.8 meters. Determine the lengths of the sides.
• 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?
• Parallelogram
  The perimeter of the parallelogram is 417 cm. The length of one side is 1.7-times longer than the length of the shorter side. What is the length of sides of a parallelogram?