# Trapezoid - hard example

Base of the trapezoid are: 24, 16 cm.
Diagonal 22, 26 cm.
Calculate its area and perimeter.

Correct result:

S =  264 cm2
o =  67.966 cm

#### Solution:

Try calculation via our triangle calculator.

$S=\dfrac{ a+c }{ 2 } \cdot \ h=\dfrac{ w }{ 2 } \cdot \ h \ \\ \ \\ h=2 \cdot \ S/w=2 \cdot \ 264/40=\dfrac{ 66 }{ 5 }=13.2 \ \text{cm} \ \\ \ \\ u^2=h^2 +a_{1}^2=13.2^2 +17.6^2=\dfrac{ 4356 }{ 25 }=174.24 \ \\ \ \\ a_{1}=\sqrt{ u^2 - h^2 }=\sqrt{ 22^2 - 13.2^2 }=\dfrac{ 88 }{ 5 }=17.6 \ \text{cm} \ \\ a_{2}=a - a_{1}=24 - 17.6=\dfrac{ 32 }{ 5 }=6.4 \ \text{cm} \ \\ \ \\ b^2=h^2 + a_{2}^2 \ \\ \ \\ b=\sqrt{ h^2 + a_{2}^2 }=\sqrt{ 13.2^2 + 6.4^2 } \doteq 14.6697 \ \text{cm} \ \\ \ \\ c_{1}=\sqrt{ v^2 - h^2 }=\sqrt{ 26^2 - 13.2^2 }=\dfrac{ 112 }{ 5 }=22.4 \ \text{cm} \ \\ c_{2}=a - c_{1}=24 - 22.4=\dfrac{ 8 }{ 5 }=1.6 \ \text{cm} \ \\ \ \\ d^2=h^2 + c_{2}^2 \ \\ \ \\ d=\sqrt{ h^2 + c_{2}^2 }=\sqrt{ 13.2^2 + 1.6^2 } \doteq 13.2966 \ \text{cm} \ \\ \ \\ \ \\ o=a+b+c+d=24+14.6697+16+13.2966=67.966 \ \text{cm}$

We would be very happy if you find an error in the example, spelling mistakes, or inaccuracies, and please send it to us. We thank you!

Tips to related online calculators

#### You need to know the following knowledge to solve this word math problem:

We encourage you to watch this tutorial video on this math problem:

## Next similar math problems:

• Four sides of trapezoid
Trapezoid is given by length of four sides: 40.5 42.5 52.8 35.0. Calculate its area.
• One trapezium
One trapezium has AB=24M, BC=36M, CD=80M, DA=80M long sides. Find the area.
• Cardboard box
We want to make a cardboard box shaped quadrangular prism with rhombic base. Rhombus has a side of 5 cm and 8 cm one diagonal long. The height of the box to be 12 cm. The box will be open at the top. How many square centimeters cardboard we need, if we ca
What is the volume of a quadrilateral oblique prism with base edges of length a = 1m, b = 1.1m, c = 1.2m, d = 0.7m, if a side edge of length h = 3.9m has a deviation from the base of 20° 35 ´ and the edges a, b form an angle of 50.5°.
• Triangular prism
Calculate the surface of a triangular prism 10 cm high, the base of which is a triangle with sides 6 cm 8 cm and 8 cm
• Annulus from triangle
Calculate the content of the area bounded by a circle circumscribed and a circle inscribed by a triangle with sides a = 25mm, b = 29mm, c = 36mm
• Sss triangle
Calculate the area and heights in the triangle ABC by sides a = 8cm, b = 11cm, c = 12cm
• Sides ratio
Calculate the circumference of a triangle with area 84 cm2 if a:b:c = 10:17:21
• Area and two angles
Calculate the size of all sides and internal angles of a triangle ABC, if it is given by area S = 501.9; and two internal angles α = 15°28' and β = 45°.
• Sides of the triangle
Calculate triangle sides where its area is S = 84 cm2 and a = x, b = x + 1, xc = x + 2
• Circular railway
The railway is to interconnect in a circular arc the points A, B, and C, whose distances are | AB | = 30 km, AC = 95 km, BC | = 70 km. How long will the track from A to C?
• Compute 4
Compute the exact value of the area of the triangle with sides 14 mi, 12 mi, and 12 mi long.
• Is right triangle or not
If right triangle ABC, have sides a=13, b=11.5, c=22.5. Find area.
• Triangle
Determine whether a triangle can be formed with the given side lengths. If so, use Heron's formula to find the area of the triangle. a = 158 b = 185 c = 201
• Find the area
Find the area of the triangle with the given measurements. Round the solution to the nearest hundredth if necessary. A = 50°, b = 30 ft, c = 14 ft
• The farmer
The farmer would like to first seed his small field. The required amount depends on the seed area. Field has a triangular shape. The farmer had fenced field, so he knows the lengths of the sides: 119, 111 and 90 meters. Find a suitable way to determine th
• Sails
We known heights 220, 165 and 132 of sail. It has triangular shape. What is the surface of the sail?