A sign is in the shape of a rhombus with a 60° angle and sides of 9 cm long. Find its area to the nearest tenth.
a. 70.1 cm2
b. 3.9 cm2
c. 7.8 cm2
d. 35.1 cm2
2007-04-26 05:44:50 · 3 answers · asked by downninjette1716 1 in Science & Mathematics ➔ Mathematics
the vertical leg of the rhombus will be 9/2*root 3 = 7.794 cm
area = 7.794*9 = 70.15 cm^2
2007-04-26 05:49:40 · answer #1 · answered by minorchord2000 6 · 0⤊ 0⤋
70.1 cm2
The rhombus has equal sides, all 9 cm
The supplementary angle is 120, bisect that and you have 2 equilateral triangles with sides of 9 in the rhombus.
Now take one of the triangles, bisect the angle by dropping a perpendicular line to the base, that also bisects the base.
When you bisect the base you end up with a right triangle with one side of 4.5 and by using the Pythagorean theorem, the angle bisector line is 7.794. Now we have enough to calculate the area of the triangle which is 1/4 the area of the rhombus. The area of one of the triangles is 17.537 cm2,
Multiply by 4 and the area of the rhombus is
70.148 cm2
2007-04-26 13:05:01 · answer #2 · answered by Robert L 7 · 0⤊ 0⤋
70.1cm (a)
2007-04-26 12:53:43 · answer #3 · answered by Anonymous · 0⤊ 0⤋