# IS trapezoid

Calculate the length of diagonal u and height v of isosceles trapezoid ABCD, whose bases have lengths a = |AB| = 37 cm, c = |CD| = 29 cm and legs b = d = |BC| = |AD| = 28 cm.

Result

v =  27.7 cm
u=|AC|=|BD| =  43.1 cm

#### Solution:

$a = 37 \ cm \ \\ c = 29 \ cm \ \\ r = 28 \ cm \ \\ x = (a-c)/2 = (37-29)/2 = 4 \ cm \ \\ v = \sqrt{ r^2-x^2 } = \sqrt{ 28^2-4^2 } = 16 \ \sqrt{ 3 } \doteq 27.7128 = 27.7 \ \text { cm }$
$u = \sqrt{ v^2+(a-x)^{ 2 } } = \sqrt{ 27.7128^2+(37-4)^{ 2 } } \doteq 43.0847 = 43.1 \ \text { cm }$

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 1 comment: Math student
I don’t know how to do it????????

1 year ago  3 Likes #### Following knowledge from mathematics are needed to solve this word math problem:

Pythagorean theorem is the base for the right triangle calculator. See also our trigonometric triangle calculator.

## Next similar math problems:

1. Right Δ A right triangle has the length of one leg 7 cm and length of the hypotenuse 25 cm. Calculate the height of the triangle. Calculate the radius of the circle whose length is 107 cm larger than its diameter
3. Medians in right triangle It is given a right triangle, angle C is 90 degrees. I know it medians t1 = 8 cm and median t2 = 12 cm. .. How to calculate the length of the sides?
4. Two chords Calculate the length of chord AB and perpendicular chord BC to circle if AB is 4 cm from the center of the circle and BC 8 cm from the center of the circle.
5. Cuboid face diagonals The lengths of the cuboid edges are in the ratio 1: 2: 3. Will the lengths of its diagonals be the same ratio? The cuboid has dimensions of 5 cm, 10 cm, and 15 cm. Calculate the size of the wall diagonals of this cuboid.
6. Body diagonal Calculate the volume of a cuboid whose body diagonal u is equal to 6.1 cm. Rectangular base has dimensions of 3.2 cm and 2.4 cm
7. Surface of the cylinder Calculate the surface of the cylinder for which the shell area is Spl = 20 cm2 and the height v = 3.5 cm
8. Voltmeter range We have a voltmeter which in the original set measures voltage to 10V. Calculate the size of the ballast resistor for this voltmeter, if we want to measure the voltage up to 50V. Voltmeter's internal resistance is 2 kiloohm/Volt.
9. Cube in a sphere The cube is inscribed in a sphere with volume 9067 cm3. Determine the length of the edges of a cube.
10. Faces diagonals If the diagonals of a cuboid are x, y, and z (wall diagonals or three faces) respectively than find the volume of a cuboid. Solve for x=1.2, y=1.7, z=1.45
11. A concrete pedestal A concrete pedestal has a shape of a right circular cone having a height of 2.5 feet. The diameter of the upper and lower bases are 3 feet and 5 feet, respectively. Determine the lateral surface area, total surface area, and the volume of the pedestal.
12. Frustum of a cone A reservoir contains 28.54 m3 of water when completely full. The diameter of the upper base is 3.5 m while at the lower base is 2.5 m. Determine the height if the reservoir is in the form of a frustum of a right circular cone.
13. Cylinder and its circumference If the height of a cylinder is 4 times its circumference. What is the volume of the cylinder in terms of its circumference, c?
14. Secret treasure Scouts have a tent in the shape of a regular quadrilateral pyramid with a side of the base 4 m and a height of 3 m. Determine the radius r (and height h) of the container so that they can hide the largest possible treasure.
15. Equation 23 Find value of unknown x in equation: x+3/x+1=5 (problem finding x)
16. Geography tests On three 150-point geography tests, you earned grades of 88%, 94%, and 90%. The final test is worth 250 points. What percent do you need on the final to earn 93% of the total points on all tests?
17. An equilateral triangle The perimeter of an equilateral triangle is 33cm. How long is each side?