Look at the rhombus in the figure.
What is its area?
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Look at the rhombus in the figure.
What is its area?
First, let's remember that according to the properties of a rhombus, all sides of a rhombus are equal,
Therefore, if we define the sides of the rhombus with the letters ABCD,
We can argue that:
AB=BC=CD=DA
We use the perimeter formula:
50 = AB+BC+CD+DA
And we can conclude that
4AB=50
(We can also use any other side, it doesn't matter in this case because they are all equal.)
We divide by four and reveal that:
AB=BC=CD=DA = 12.5
Now let's remember the formula for the area of a rhombus: the height times the side corresponding to the height.
We are given the length of the external height 8,
Now, we can replace in the formula:
8*12.5=100
100 cm²
Given the rhombus in the figure
What is your area?
The height is the perpendicular distance between parallel sides, while a diagonal connects opposite vertices. In this problem, the length 8 is the external height, not a diagonal!
The number 8 represents the height (perpendicular distance), not a side length. The side length comes from dividing the perimeter: 50 ÷ 4 = 12.5.
Use Area = height × side when given perimeter and height. Use Area = (d₁ × d₂) ÷ 2 only when you have both diagonal lengths.
Double-check: if perimeter = 50 and all sides are equal, then each side = 50 ÷ 4 = 12.5. Verify: 12.5 × 4 = 50 ✓
Yes! You can use height × side or (diagonal₁ × diagonal₂) ÷ 2. Both give the same answer, but you need different given information for each method.
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