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 ABC and ACD triangles in centimeters.

Correct result:

S =  2883 cm²
x =  62 cm

Solution:

$u=62 \ \text{cm} \ \\ a=\sqrt{ u^2+u^2 }=\sqrt{ 62^2+62^2 } \doteq 62 \ \sqrt{ 2 } \ \text{cm} \doteq 87.6812 \ \text{cm} \ \\ \ \\ c^2 + c^2=u^2 \ \\ c=u / \sqrt{ 2 }=62 / \sqrt{ 2 } \doteq 31 \ \sqrt{ 2 } \ \text{cm} \doteq 43.8406 \ \text{cm} \ \\ \ \\ S=\dfrac{ a+c }{ 2 } \cdot \ c=\dfrac{ 87.6812+43.8406 }{ 2 } \cdot \ 43.8406=2883 \ \text{cm}^2$

$o_{1}=2 \cdot \ c + u=2 \cdot \ 43.8406 + 62 \doteq 149.6812 \ \text{cm} \ \\ o_{2}=2 \cdot \ u + a=2 \cdot \ 62 + 87.6812 \doteq 211.6812 \ \text{cm} \ \\ \ \\ x=o_{2}-o_{1}=211.6812-149.6812=62 \ \text{cm}$

Try another example

Showing 0 comments:

Next similar math problems:

• Horses playground
  The fence for the horses has the shape of a rectangular trapezoid with an area of 400 m², the base lengths should be 31 m and 19 m. How many meters of boards will they need to fence it if the boards are stacked in 5 rows?
• Trapezoid - RR
  Find the area of the right angled trapezoid ABCD with the right angle at the A vertex; a = 3 dm b = 5 dm c = 6 dm d = 4 dm
• Trapezium ABCD
  In the figure, ABDC is a trapezium in which AB || CD. line segments RN and LM are drawn parallel to AB such that AJ=JK=KP. If AB=0.5m and AP=BQ=1.8m, find the lengths of AC, BD, RN and LM. angle D=angle C=60
• Isosceles trapezium
  Calculate the area of an isosceles trapezium ABCD if a = 10cm, b = 5cm, c = 4cm.
• Isosceles
  Isosceles trapezium ABCD ABC = 12 angle ABC = 40 ° b=6. Calculate the circumference and area.
• Land - isosceles trapezoid
  Calculate the content and perimeter of the building plot in the form of an isosceles trapezoid with bases 120m, 95m and height 50m.
• The ditch
  Ditch with a cross-section of an isosceles trapezoid with bases 2m and 6m are deep 1.5m. How long is the slope of the ditch?
• Length IT
  Find the length (circumference) of an isosceles trapezoid in which the length of the bases a,c and the height h are given: a = 8 cm c = 2 cm h = 4 cm
• Isosceles trapezoid
  The lengths of the bases of the isosceles trapezoid are in the ratio 5:3, the arms have a length of 5 cm and height = 4.8 cm. Calculate the circumference and area of a trapezoid.
• ISO Triangle V2
  Perimeter of RR triangle (isosceles) is 474 m and the base is 48 m longer than the arms. Calculate the area of this triangle.
• Isosceles III
  The base of the isosceles triangle is 17 cm area 416 cm². Calculate the perimeter of this triangle.
• Holidays - on pool
  Children's tickets to the swimming pool stands x € for an adult is € 2 more expensive. There was m children in the swimming pool and adults three times less. How many euros make treasurer for pool entry?
• Reference angle
  Find the reference angle of each angle:
• Spruce height
  How tall was spruce that was cut at an altitude of 8m above the ground and the top landed at a distance of 15m from the heel of the tree?
• An observer
  An observer standing west of the tower sees its top at an altitude angle of 45 degrees. After moving 50 meters to the south, he sees its top at an altitude angle of 30 degrees. How tall is the tower?
• RT 11
  Calculate the area of right tirangle if its perimeter is p = 45 m and one cathethus is 20 m long.
• Difference of legs
  In a right triangle, the length of the hypotenuse is 65 m, and the difference of legs is 23 m. Calculate the perimeter of this triangle.