Answer:
The triangles in figures A , D have an area of 22.5 units²
Step-by-step explanation:
* Lets explain how to solve the problem
- The area of any triangle is A = 1/2 bh , where b is the base of the
triangle and h is the height of this base
- The horizontal line has same y-coordinates of its endpoints
- The vertical line has same x-coordinates of its endpoints
- In the Cartesian coordinates the length of any horizontal line is the
difference between the x-coordinates of its endpoints and the length
of any vertical line is the difference between the y-coordinates of
its endpoints
* Lets solve the problem
# Figure A
∵ The vertices of the triangles are (-5 , 0) , (10 , 0) , (-1 , 3)
∵ the end points of its base are (-5 , 0) , (10 , 0)
∵ The base of the triangle = 10 - (-5) = 10 + 5 = 15 units
∵ The height of the triangle is the difference between the
y-coordinates of its vertex and the y-coordinate of its base
∵ The y-coordinate of the vertex is 3
∵ The y-coordinate of the base is 0
∴ The height of the triangle = 3 - 0 = 3 units
∴ Its A = 1/2 (15)(3) = 22.5 units²
* The triangle in figure A has an area of 22.5 units²
# Figure B
∵ The vertices of the triangles are (-1 , -1) , (-6 , -1) , (-2 , -8)
∵ the end points of its base are (-1 , -1) , (-6 , -1)
∵ The base of the triangle = -1 - (-6) = -1 + 6 = 5 units
∵ The height of the triangle is the difference between the
y-coordinates of its vertex and the y-coordinate of its base
∵ The y-coordinate of the vertex is -8
∵ The y-coordinate of the base is -1
∴ The height of the triangle = -1 - (-8) = -1 + 8 = 7 units
∴ Its A = 1/2 (5)(7) = 17.5 units²
* The triangle in figure B has an area of 17.5 units²
# Figure C
∵ The vertices of the triangles are (-9 , 2) , (-1 , 2) , (-7 , 8)
∵ the end points of its base are (-9 , 2) , (-1 , 2)
∵ The base of the triangle = -1 - (-9) = -1 + 9 = 8 units
∵ The height of the triangle is the difference between the
y-coordinates of its vertex and the y-coordinate of its base
∵ The y-coordinate of the vertex is 8
∵ The y-coordinate of the base is 2
∴ The height of the triangle = 8 - 2 = 6 units
∴ Its A = 1/2 (8)(6) = 24 units²
* The triangle in figure C has an area of 24 units²
# Figure D
∵ The vertices of the triangles are (0 , 0) , (0 , -9) , (5 , -7)
∵ the end points of its base are (0 , 0) , (0 , -9)
∵ The base of the triangle = 0 - (-9) = 0 + 9 = 9 units
∵ The height of the triangle is the difference between the
x-coordinates of its vertex and the x-coordinate of its base
∵ The x-coordinate of the vertex is 5
∵ The x-coordinate of the base is 0
∴ The height of the triangle = 5 - 0 = 5 units
∴ Its A = 1/2 (5)(9) = 22.5 units²
* The triangle in figure D has an area of 22.5 units²
∴ The triangles in A , D have an area of 22.5 units²
