Find the area of the rhombus. Round to the nearest tenth if necessary.
M(0,4), N(3,0), P(0,-3), Q(-3,0)
triangle above x axis
base = 6
height = 4
(1/2) b h = 3*4 = 12
triangle below x axis
base = 6
height = 3
(1/2) b h = 3*3 = 9
9 + 12 = 21
By the way - rhombus?
Maybe M was supposed to be at (0,3) ?
I just went back and checked... I should have written quadrilateral...thank you!
To find the area of a rhombus, we can use the formula: Area = (diagonal1 * diagonal2) / 2.
First, let's find the lengths of the diagonals of the rhombus using the given coordinates of the vertices, M(0,4), N(3,0), P(0,-3), and Q(-3,0).
The length of diagonal MN can be found using the distance formula:
d = √[(x2 - x1)^2 + (y2 - y1)^2].
For MN, the coordinates are (0,4) and (3,0):
dMN = √[(3 - 0)^2 + (0 - 4)^2]
= √[9 + 16]
= √25
= 5.
Similarly, the length of diagonal PQ can be found using the distance formula:
dPQ = √[(-3 - 0)^2 + (0 - (-3))^2]
= √[9 + 9]
= √18.
Now, let's substitute these values into the formula for the area of a rhombus:
Area = (diagonal1 * diagonal2) / 2
= (5 * √18) / 2
= 5√18 / 2.
If we need to round the result to the nearest tenth, we can approximate √18 as 4.2 (rounded to one decimal place):
Area ≈ (5 * 4.2) / 2
≈ 21 / 2
≈ 10.5.
Therefore, the area of the rhombus, rounded to the nearest tenth, is approximately 10.5 square units.