Find the height of a rhombus whose area is $300 cm^2$ and base area is $20 cm^2$.
Answer (2)
We are given the area and base of a rhombus.
We use the formula for the area of a rhombus: A re a = ba se × h e i g h t .
We substitute the given values into the formula and solve for the height: 300 = 20 × h e i g h t , so h e i g h t = 20 300 .
We calculate the height: h e i g h t = 15 c m .
Explanation
Problem Analysis and Given Data We are given a rhombus with an area of 300 c m 2 and a base of 20 c m . We need to find the height of the rhombus. The area of a rhombus can be calculated using the formula:
A re a = ba se × h e i g h t
In our case, we have:
A re a = 300 c m 2 ba se = 20 c m h e i g h t = h (what we need to find)
Applying the Area Formula Now, we can plug in the given values into the area formula:
300 = 20 × h
Isolating the Height To find the height (h), we need to isolate it by dividing both sides of the equation by the base (20):
h = 20 300
Calculating the Height Now, we perform the division:
h = 15
Final Answer So, the height of the rhombus is 15 cm.
Examples
Understanding the area and height relationship in a rhombus is useful in various real-life scenarios. For example, if you're designing a kite in the shape of a rhombus and you know the desired area and the length of the base, you can calculate the height needed to achieve that area. This ensures your kite has the correct dimensions for optimal flight. Similarly, in construction, if you're tiling a floor with rhombus-shaped tiles and you know the area you want to cover and the base length of the tiles, you can determine the height of the tiles needed to cover the area efficiently.
The height of the rhombus is 15 cm, calculated using the area formula by isolating the height. Given an area of 300 cm² and a base of 20 cm, we derived the height through division. Therefore, the height required to achieve this area is 15 cm.
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