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.

Correct result:

S =  36 cm²

Solution:

$$\begin{gathered} a=8\text{ cm } \\ h=6\text{ cm } \\ {h}_1=4\text{ cm } \\ {h}_2=h-h_1=6-4=2\text{ cm } \\ a:c=h_1:h_2 \\ c=a\cdot {\displaystyle \frac{h_2}{h_1}}=8\cdot {\displaystyle \frac{2}{4}}=4\text{ cm } \\ S={\displaystyle \frac{a+c}{2}}\cdot h={\displaystyle \frac{8+4}{2}}\cdot 6=36{\text{cm}}^2 \end{gathered}$$

Try another example

Showing 0 comments:

Next similar math problems:

• 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.
• 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?
• Segment in a triangle
  In a triangle ABC with the side/AB/ = 24 cm is constructed middle segment/DE/ = 18 cm parallel to the side AB at a distance 1 cm from AB. Calculate the height of the triangle ABC to side AB.
• Trapezoid
  Area of trapezoid is 135 cm². Sides a, c and height h are in a ratio 6:4:3. How long are a,c and h? Make calculation...
• Diagonal
  he rectangular ABCD trapeze, whose AD arm is perpendicular to the AB and CD bases, has area 15cm square. Bases have lengths AB = 6cm, CD = 4cm. Calculate the length of the AC diagonal.
• Rhombus and diagonals
  The a rhombus area is 150 cm² and the ratio of the diagonals is 3:4. Calculate the length of its height.
• Ratio in trapezium
  The height v and the base a, c in the trapezoid ABCD are in the ratio 1: 6: 3, its content S = 324 square cm. Peak angle B = 35 degrees. Determine the perimeter of the trapezoid
• 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.
• Rectangular trapezoid
  The rectangular trapezoid ABCD is: /AB/ = /BC/ = /AC/. The length of the median is 6 cm. Calculate the circumference and area of a trapezoid.
• 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?
• Trapezium
  The length of the base and the height size of the base of the trapezium is at ratio 5:3:2, the content area of the trapezium is 128 cm². Calculate the length of the base and the height of the trapezoid.
• Isosceles trapezium
  Calculate the area of an isosceles trapezium ABCD if a = 10cm, b = 5cm, c = 4cm.
• 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?
• Trapezium
  The area of trapezium is 35 cm². Find its altitude if the bases are 6cm and 8 cm.
• Rectangle 3-4-5
  The sides of the rectangle are in a ratio of 3:4. The length of the rectangle diagonal is 20 cm. Calculate the content of the rectangle.
• The bases
  The bases of the isosceles trapezoid ABCD have lengths of 10 cm and 6 cm. Its arms form an angle α = 50˚ with a longer base. Calculate the circumference and content of the ABCD trapezoid.
• 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.