The area of the considered 3 triangles is given by: Option B: 13 sq. units.
<h3>How to find the area of a triangle whose vertices' coordinates are given?</h3>
Suppose the vertices of the considered triangle ABC are on , then, the area of the triangle is given by:
For this case, the missing image is attached below.
The second and third triangle are easy as their base and height are parallel to x or y axis.
We will find area of third triangle by coordinates of its vertices.
Getting area of first triangle:
- Coordinates of A : (4,10)
- Coordinates of B : (5,7)
- Coordinates of C : (7,8)
Thus, we get:
Area of second triangle = base, and h is the perpendicular line connecting from line RS and the vertex T
From figure we see:
|RS| = 3 units, h = 3 units
Thus, area of second triangle =
Area of third triangle = where XY is base, and h is the perpendicular line connecting from line XY and the vertex Z
From figure we see:
|XY| = 5 units, h = 2 units
Thus, Area of third triangle =
Total area = 3.5 + 4.5 + 5 = 13 sq. units
Thus, the area of the considered 3 triangles is given by: Option B: 13 sq. units.
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