Parallelogram

The sides of the parallelogram are 8 cm and 6 cm long and the angle of the diagonals is 60°. What is its area?

Correct answer:

S =  66.954 cm²

Step-by-step explanation:

$$\begin{gathered} a=8\text{ cm } \\ b=6\text{ cm } \\ X=60^{\circ } \\ Y=180-X=180-60=120^{\circ } \\ {S}_1=\mathrm{\Delta }BCS=b-b-b \\ {S}_2=\mathrm{\Delta }BSA=a-b-b \\ {S}_1=\sqrt{3}\mathrm{/}4\cdot b^2=\sqrt{3}\mathrm{/}4\cdot 6^2=9\sqrt{3}{\text{cm}}^2\doteq 15.5885{\text{cm}}^2 \\ s={\displaystyle \frac{a+b+b}{2}}={\displaystyle \frac{8+6+6}{2}}=10\text{ cm } \\ {S}_2=\sqrt{s\cdot (s-a)\cdot (s-b)\cdot (s-b)}=\sqrt{10\cdot (10-8)\cdot (10-6)\cdot (10-6)}=8\sqrt{5}{\text{cm}}^2\doteq 17.8885{\text{cm}}^2 \\ S=2\cdot S_1+2\cdot S_2=2\cdot 15.5885+2\cdot 17.8885=66.954{\text{cm}}^2 \end{gathered}$$

Try another example

Related math problems and questions:

• Two chords
  From the point on the circle with a diameter of 8 cm, two identical chords are led, which form an angle of 60°. Calculate the length of these chords.
• Viewing angle
  The observer sees a straight fence 60 m long at a viewing angle of 30°. It is 102 m away from one end of the enclosure. How far is the observer from the other end of the enclosure?
• Triangle SAS
  Calculate the triangle area and perimeter, if the two sides are 51 cm and 110 cm long and angle them clamped is 130 °.
• Diagonals in diamond
  In the rhombus is given a = 160 cm, alpha = 60 degrees. Calculate the length of the diagonals.
• Parallelogram diagonals
  Find the area of a parallelogram if the diagonals u1 = 15 cm, u2 = 12 cm and the angle formed by them is 30 degrees.
• Diagonals
  Calculate the length of the rhombus's diagonals if its side is long 5 and one of its internal angles is 80°.
• 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
• Triangle's centroid
  In the triangle ABC the given lengths of its medians tc = 9, ta = 6. Let T be the intersection of the medians (triangle's centroid) and point is S the center of the side BC. The magnitude of the CTS angle is 60°. Calculate the length of the BC side to 2 d
• The pond
  We can see the pond at an angle 65°37'. Its end points are 155 m and 177 m away from the observer. What is the width of the pond?
• Two groves
  Two groves A, B are separated by a forest, both are visible from the hunting grove C, which is connected to both by direct roads. What will be the length of the projected road from A to B, if AC = 5004 m, BC = 2600 m and angle ABC = 53° 45 ’?
• Inner angles
  The inner angles of the triangle are 30°, 45° and 105° and its longest side is 10 cm. Calculate the length of the shortest side, write the result in cm up to two decimal places.
• Calculate triangle
  In the triangle ABC, calculate the sizes of all heights, angles, perimeters and its area, if given a-40cm, b-57cm, c-59cm
• Parallelogram ABCD
  We have the parallelogram ABCD, where AB is 6.2 cm BC is 5.4 cm AC is 4.8 cm calculate the height on the AB side and the angle DAB
• Children playground
  The playground has a trapezoid shape, and the parallel sides have a length of 36 m and 21 m. The remaining two sides are 14 m long and 16 m long. Find the size of the inner trapezoid angles.
• Diagonals of the rhombus
  How long are the diagonals e, f in the diamond, if its side is 5 cm long and its area is 20 cm²?
• Triangle from median
  Calculate the perimeter, content, and magnitudes of the triangle ABC's remaining angles, given: a = 8.4; β = 105° 35 '; and median ta = 12.5.
• Largest angle of the triangle
  Calculate the largest angle of the triangle whose sides have the sizes: 2a, 3/2a, 3a