A parallelogram has two adjacent sides of length 4cm and 6cm reapectively. If the included angle measures 52 degrees, find the area of the parallelogram.
the length of two adjacent sides of a parallelogram are 5cm ,4cm respectively.if the length of one diagonal is 7cm . then what will be the length of the other diagonal???
Well, a parallelogram is just a fancy way of saying "a lazy rectangle". It's like a rectangle that's leaning back on a recliner chair, enjoying life.
To find the area of a parallelogram, you just multiply the base (the side with length 6cm) by the height. But here's the twist, the height is not the other adjacent side! It's actually the perpendicular distance from the base to the opposite side.
Now, imagine a little triangle chilling inside the parallelogram. The base of the triangle is 4cm, one side is 6cm (that's the adjacent side not the base), and the angle between them is 52 degrees.
Now, let's do some math magic to find the height of the parallelogram (the distance from the base to the opposite side). We can use trigonometry, specifically the sine function.
sin(52°) = height/6cm
So, the height is 6cm multiplied by sin(52°). Plug this value into the formula for finding the area of a parallelogram, and you'll get your answer. Voila!
To find the area of a parallelogram, we can use the formula:
Area = base * height
In this case, the length of the base is given by the shorter side, which is 4cm.
To find the height, we can use the given information about the included angle. The height is the perpendicular distance between the base and the opposite side.
Here's how we can find the height:
1. Draw a perpendicular from one of the endpoints of the longer side (6cm) to the base (4cm). This forms a right-angled triangle.
2. The given included angle is 52 degrees. We can use this angle and the known sides of the triangle to find the height.
3. Looking at the triangle, we have the adjacent side (4cm) and the opposite side (height). We can use the trigonometric function tangent to find the height.
tan(angle) = opposite / adjacent
tan(52) = height / 4
Rearranging the equation, we get:
height = 4 * tan(52)
4. Calculate the value of the height using a calculator:
height ≈ 4 * 1.2799
height ≈ 5.1196 cm
Now that we have the base (4cm) and the height (5.1196cm), we can substitute these values into the formula for the area of a parallelogram:
Area = base * height
Area = 4 * 5.1196
Area ≈ 20.4784 square cm
Therefore, the area of the parallelogram is approximately 20.4784 square cm.
453cm2
18.91
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area = (4)(6)sin52°
= ....