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.

Correct result:

S =  71.5542 cm²

Solution:

$$\begin{gathered} a:c=5:3 \\ b=6\text{ cm } \\ d=b=6=6\text{ cm } \\ h=4\text{ cm } \\ x=\sqrt{b^2-h^2}=\sqrt{6^2-4^2}=2\sqrt{5}\text{ cm}\doteq 4.4721\text{ cm } \\ a=x+c+x \\ 3a=5c \\ 3\cdot (c+2x)=5c \\ 3c+6x=5c \\ 2c=6x \\ c=3\cdot x=3\cdot 4.4721=6\sqrt{5}\text{ cm}\doteq 13.4164\text{ cm } \\ a=5\mathrm{/}3\cdot c=5\mathrm{/}3\cdot 13.4164=10\sqrt{5}\text{ cm}\doteq 22.3607\text{ cm } \\ S=(a+c)\cdot h\mathrm{/}2=(22.3607+13.4164)\cdot 4\mathrm{/}2=32\sqrt{5}\doteq 71.5542=71.5542{\text{cm}}^2 \\ \text{ Verifying Solution: } \\ {k}_1={\displaystyle \frac{a}{c}}={\displaystyle \frac{22.3607}{13.4164}}={\displaystyle \frac{5}{3}}\doteq 1.6667 \end{gathered}$$

Try another example

Showing 0 comments:

Next similar math problems:

• Railway embankment
  The section of the railway embankment is an isosceles trapezoid, the sizes of the bases of which are in the ratio 5: 3. The arms have a length of 5 m and the height of the embankment is 4.8 m. Calculates the size of the embankment section area.
• 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
• 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?
• 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 - 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.
• 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.
• 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.
• 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.
• 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...
• Trapezoid RT
  The plot has a shape of a rectangular trapezium ABCD, where ABIICD with a right angle at the vertex B. side AB has a length 36 m. The lengths of the sides AB and BC are in the ratio 12:7. Lengths of the sides AB and CD are a ratio 3:2. Calculate consumpti
• Orchard
  Route passes trapezoidal orchard perpendicular to the parallel sides. It is 80 cm wide. The lengths of the bases are in the ratio 5:3 and the length of the longer base to the length of the path is in the ratio 5:6. How many square meters occupies the rout
• 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?
• Trapezoid - central median
  The central median divides the trapezoid into two smaller trapezoids. Determines the ratio of their contents.
• 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
• 120 nuts
  Divide 120 nuts in a ratio of 4: 6.
• Proportional relationship
  The ordered pairs (6,24) and (1, s) represent a proportional relationship. Find the value of s.
• Trapezoid 25
  Trapezoid PART with AR||PT has (angle P=x) and (angle A=2x) . In addition, PA = AR = RT = s. Find the length of the median of Trapezoid PART in terms of s.