Sharon made a scale drawing of a triangular park. The coordinates for the vertices of
the park are:
(– 10, 5)
(15, 5)
(10, 12)
Her scale is 1 unit = 1 meter.
What is the area of the triangular park in square meters?
Calculate the determinant (3 x 3 matrix). Then divide it by two and get the absolute value. That's the area.
Let the z-coordinate be equal to 1:
-10 | 5 | 1
15 | 5 | 1
10 | 12 | 1
The determinant of this set up is 175.
Area is therefore, | 175/2 | = 87.5 units
Hope this helps~ `u`
To find the area of the triangular park, we can use the formula for the area of a triangle: A = (1/2) * base * height.
In this case, since the coordinates of the vertices are given, we can find the base and height of the triangle by calculating the lengths of the sides. Once we have the base and height, we can plug them into the formula to find the area.
Let's start with finding the base. The base of the triangle is the distance between the points (– 10, 5) and (15, 5). To calculate this, we can subtract the x-coordinates of the points:
Base = |15 - (-10)| = 25
Next, let's find the height. The height of a triangle is the perpendicular distance from the base to the opposite vertex. In this case, the opposite vertex is (10, 12). To calculate the height, we need to find the vertical distance between the base and the opposite vertex.
Height = |12 - 5| = 7
Now that we have the base and height, we can plug them into the formula to find the area:
A = (1/2) * base * height
= (1/2) * 25 * 7
= 87.5 square meters
Therefore, the area of the triangular park is 87.5 square meters.