In the parallelogram PQRS, PQ = 8cm and angle SPQ = 30 degrees
If the area of the parallelogram is 24 square centimeters, find its perimeter.
the altitude h is 8 sin30 = 4
So, the base b can be found by
bh = 24
anxd then, of course, the perimeter p = 2(8+b)
To find the perimeter of the parallelogram, we first need to determine the length of the other sides.
In a parallelogram, opposite sides are equal in length. Therefore, PS = 8 cm.
We also know that the area of the parallelogram is 24 square centimeters.
The area of a parallelogram can be calculated using the formula: Area = base x height.
In our case, the base is PQ = 8 cm, and the height is PS.
So, we can rearrange the formula to find the height: Height = Area / Base.
Substituting the values, we have: Height = 24 cm² / 8 cm = 3 cm.
Since the angle SPQ is 30 degrees, we can use trigonometry to find the length of the height, PS.
In a right-angled triangle, the height, PS, can be found using the formula: Height = PQ x sin(angle SPQ).
Substituting the values, we have: PS = 8 cm x sin(30 degrees) = 8 cm x 0.5 = 4 cm.
Therefore, PS = 4 cm.
Now, we have all the sides of the parallelogram: PQ = 8 cm, QR = 8 cm, RS = 4 cm, and SP = 4 cm.
To find the perimeter of the parallelogram, we can add all the sides together.
Perimeter = PQ + QR + RS + SP = 8 cm + 8 cm + 4 cm + 4 cm = 24 cm.
Therefore, the perimeter of the parallelogram is 24 centimeters.