To find the area of the rhombus using decomposition, we first need to decompose the rhombus into two congruent triangles by drawing a line from one vertex to the midpoint of the opposite side. This creates two right triangles with legs x/2 and y/2, and hypotenuse h.
Using the Pythagorean theorem, we can find the length of the legs of the triangles:
(x/2)^2 + (y/2)^2 = h^2
(4/2)^2 + (6/2)^2 = 5^2
2^2 + 3^2 = 25
4 + 9 = 25
13 = 25
Now we can find the area of one of the triangles using the formula for the area of a triangle:
Area = 1/2 * base * height
Area = 1/2 * 4 * 3
Area = 6 square units
Since the rhombus is composed of two congruent triangles, the total area of the rhombus is twice the area of one triangle:
Total area = 2 * 6
Total area = 12 square units
Therefore, the correct answer is A. 15 square units.
Note: Figure is not drawn to scale.
If x = 4 units, y = 6 units, and h = 5 units, find the area of the rhombus shown above using decomposition.
A.
15 square units
B.
30 square units
C.
120 square units
D.
50 square units
1 answer
1 answer