One trapezium

One trapezium has AB=24M, BC=36M, CD=80M, DA=80M long sides. Find the area.

Correct answer:

A =  1633.8636 m²

Step-by-step explanation:

$$\begin{gathered} a=24\text{ m } \\ b=36\text{ m } \\ c=80\text{ m } \\ d=80\text{ m } \\ x=c-a=80-24=56\text{ m } \\ s={\displaystyle \frac{x+b+d}{2}}={\displaystyle \frac{56+36+80}{2}}=86\text{ m } \\ {S}_1=\sqrt{s\cdot (s-x)\cdot (s-b)\cdot (s-d)}=\sqrt{86\cdot (86-56)\cdot (86-36)\cdot (86-80)}=60\sqrt{215}{\text{m}}^2\doteq 879.7727{\text{m}}^2 \\ {S}_1=xh\mathrm{/}2 \\ h=2\cdot S_1\mathrm{/}x=2\cdot 879.7727\mathrm{/}56\doteq 31.4205\text{ m } \\ A={\displaystyle \frac{a+c}{2}}\cdot h={\displaystyle \frac{24+80}{2}}\cdot 31.4205=1633.8636{\text{m}}^2 \end{gathered}$$

Try another example

Showing 1 comment:

Math student

m<abc = 60 degrees
m<def = 30 degrees

Are these angles complementary

1 month ago  Like

Related math problems and questions:

• The sides 2
  The sides of a trapezoid are in the ratio 2:5:8:5. The trapezoid’s area is 245. Find the height and the perimeter of the trapezoid.
• R Trapezium
  Rectangular trapezium has bases 21 and 10 and area 92 cm². What is its perimeter?
• The trapezium
  The trapezium is formed by cutting the top of the right-angled isosceles triangle. The base of the trapezium is 10 cm and the top is 5 cm. Find the area of trapezium.
• Triangle
  Determine whether we can make a triangle with the given side lengths. If so, use Heron's formula to find the area of the triangle. a = 158 b = 185 c = 201
• Triangle ABC
  Calculate the sides of triangle ABC with area 1404 cm² and if a: b: c = 12:7:18
• 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.
• Triangle
  The triangle has known all three sides: a=5.5 m, b=5.3 m, c= 7.8 m. Calculate area of ​this triangle.
• Four sides of trapezoid
  Trapezoid is given by length of four sides: 40.5 42.5 52.8 35.0. Calculate its area.
• Trapezoid
  Calculate the area of trapezoid ABCD with sides |AD|= 68 cm, |DC|=35 cm, |CB|=12 cm, |AB|=35 cm..
• Trapezium
  The lengths of parallel sides of a trapezium are (2x+3) and (x+8), and the distance between them is (x+4). if the area of the trapezium is 590, find the value of x.
• Heron backlaw
  Calculate missing side in a triangle with sides 17 and 34 and area 275.
• 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.
• 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...
• Is right triangle or not
  If right triangle ABC, have sides a=13, b=11.5, c=22.5. Find area.
• Trapezium
  The area of trapezium is 35 cm². Find its altitude if the bases are 6cm and 8 cm.
• ISO trapezium
  Calculate area of isosceles trapezoid with base 95 long, leg 27 long and with the angle between the base and leg 70 degrees.
• Triangle
  Calculate heights of the triangle ABC if sides of the triangle are a=82, b=44, and c=53.