△ABC has vertices A(−6,5), B(−2,5), and C(−6,0).
What is the area of △ABC?
20 units2
9 units2
14 units2
10 units2
im not sure what it is can someone help????
The base length is from -6 to -2, which is 4 units...
The height is from (-6,0) up to (-6,5)
Hope this helps : )
so what is the answer?
To find the area of a triangle, we can use the formula:
Area = 1/2 * base * height
In this case, we can use the coordinates of the vertices to find the lengths of the base and the height.
The base of the triangle can be found by finding the distance between points A and B. We can use the distance formula:
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
In this case, the coordinates of points A and B are A(-6,5) and B(-2,5). Plugging the values into the formula, we get:
distance_AB = sqrt((-2 - (-6))^2 + (5 - 5)^2)
= sqrt(4^2 + 0^2)
= sqrt(16)
= 4
So, the length of the base, AB, is 4 units.
The height of the triangle can be found by finding the distance between points B and C. Using the distance formula again:
distance_BC = sqrt((-6 - (-2))^2 + (0 - 5)^2)
= sqrt(4^2 + (-5)^2)
= sqrt(16 + 25)
= sqrt(41)
So, the length of the height, BC, is sqrt(41) units.
Now, we can plug the values into the area formula:
Area = 1/2 * base * height
= 1/2 * 4 * sqrt(41)
= 2 * sqrt(41)
Now, we need to simplify the expression. Since sqrt(41) cannot be simplified further, we can leave the answer as:
Area = 2 * sqrt(41) units^2
Comparing this with the given options, we can see that none of the options match our calculated area. It's possible that there may be an error in the given options, or in the given coordinates of the triangle. Please double-check the information provided.
sketch it out : )
Then it is base length x height and then divided by 2
Once you have the picture you can find the measurements.
(AB)^2 = (-2+6)^2 + (5-5)^2 = 16.
AB = 4.
(BC)^2 = (-6+2)^2 + (0-5)^2 = 41,
BC = sqrt41. = 6.4.
(AC)^2 = (-6+6)^2 + (0-5)^2 = 25,
AC = 5.
(5/2)^2 + h^2 = 6.4^2,
h = 5.89.
A = hb/2 = 5.89*5/2 = 14.7.