Question

In rhombus ABCD, AB=12 and AC=22. Find the area of the rhombus to the nearest 10.

a) 195
b) 221.3
c) 105.5
d) 100.8

Answer 1

c) 105.5 square units

Explanation:

The area of a rhombus can be computed as half the product of the diagonal lengths.

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Half the diagonal BD will be one leg of the right triangle formed by the diagonals and the sides of the rhombus. The length of that leg is found using the Pythagorean theorem:

a² +b² = c²

11² +b² = 12²

b² = 144 -121 = 23

b = √23 ≈ 4.796

This value is half the length of diagonal BD, so multiplying it by the length of diagonal AC will give the area of the rhombus.

Area = 1/2(AC)(BD) = (22)(4.796) ≈ 105.5 . . . . square units