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

Correct answer:

S =  831.0003 mm²

Step-by-step explanation:

$$\begin{gathered} a=25\text{ mm } \\ b=29\text{ mm } \\ c=36\text{ mm } \\ {c}_1=\sqrt{a^2+b^2}=\sqrt{25^2+29^2}=\sqrt{1466}\text{ mm}\doteq 38.2884\text{ mm } \\ {c}_1\mathrm{\ne }c \\ s={\displaystyle \frac{a+b+c}{2}}={\displaystyle \frac{25+29+36}{2}}=45\text{ mm } \\ A=\sqrt{s\cdot (s-a)\cdot (s-b)\cdot (s-c)}=\sqrt{45\cdot (45-25)\cdot (45-29)\cdot (45-36)}=360{\text{mm}}^2 \\ R={\displaystyle \frac{a\cdot b\cdot c}{4\cdot A}}={\displaystyle \frac{25\cdot 29\cdot 36}{4\cdot 360}}={\displaystyle \frac{145}{8}}=18.125\text{ mm } \\ r={\displaystyle \frac{A}{s}}={\displaystyle \frac{360}{45}}=8\text{ mm } \\ {S}_1=\pi \cdot R^2=3.1416\cdot 18.125^2\doteq 1032.0623{\text{mm}}^2 \\ {S}_2=\pi \cdot r^2=3.1416\cdot 8^2\doteq 201.0619{\text{mm}}^2 \\ S=S_1-S_2=1032.0623-201.0619=831.0003{\text{mm}}^2 \end{gathered}$$

Try another example

Related math problems and questions:

• Circles 2
  Calculate the area bounded by the circumscribed and inscribed circle in triangle with sides 12 cm, 14 cm, 18 cm.
• Annulus
  Two concentric circles form an annulus of width 10 cm. The radius of the smaller circle is 20 cm. Calculate the content area of annulus.
• Heron backlaw
  Calculate missing side in a triangle with sides 17 and 34 and area 275.
• Circle and rectangle
  A rectangle with sides of 11.7 cm and 175 mm is described by circle. What is its length? Calculate the content area of the circle described by this circle.
• Desribed circle to rectangle
  Rectangle with sides 6 cm and 4 cm was circumscribed circle. What part of the content of the circle determined by the circumscribed circle occupies a rectangle? Express in perctentages(%).
• Circular ring
  Square with area 16 centimeters square are inscribed circle k1 and described circle k2. Calculate the area of circular ring, which circles k1, k2 form.
• Pentadecagon
  Calculate the content of a regular 15-sides polygon inscribed in a circle with radius r = 4. Express the result to two decimal places.
• Rectangle and circle
  The rectangle ABCD has side lengths a = 40 mm and b = 30 mm and is circumscribed by a circle k. Calculate approximately how many cm is circle long.
• Park
  In the newly built park will be permanently placed a rotating sprayer irrigation of lawns. Determine the largest radius of the circle which can irrigate by sprayer P so not to spray park visitors on line AB. Distance AB = 55 m, AP = 36 m and BP = 28 m.
• Circumscription
  Calculate radius of the Circumscribed circle in the rectangle with sides 20 and 19. It can be rectangle inscribed by circle?
• RT - inscribed circle
  In a rectangular triangle has sides lengths> a = 30cm, b = 12.5cm. The right angle is at the vertex C. Calculate the radius of the inscribed circle.
• The coil
  How many ropes (the diameter 8 mm) fit on the coil (threads are wrapped close together) The coil has dimension: the inner diameter 400mm, the outside diameter 800mm and the length of the coil is 470mm
• Triangle
  Calculate heights of the triangle ABC if sides of the triangle are a=82, b=44, and c=53.
• Four sides of trapezoid
  Calculate the area of the ABCD trapezoid with sides a = 65 cm, b = 29 cm, c = 40 cm, d = 36 cm
• 30-gon
  At a regular 30-gon the radius of the inscribed circle is 15cm. Find the "a" side size, circle radius "R", circumference, and content area.
• Reverse Pythagorean theorem
  Given are lengths of the sides of the triangles. Decide which one is rectangular: Δ ABC: 77 dm, 85 dm, 36 dm ... Δ DEF: 55 dm, 82 dm, 61 dm ... Δ GHI: 24 mm, 25 mm, 7 mm ... Δ JKL: 32 dm, 51 dm, 82 dm ... Δ MNO: 51 dm, 45 dm,
• Circles
  The area of a circle inscribed in a square is 14. What is the area of a circle circumscribed around a square?