# The vertices of triangle ABC are A(-4,0), B(2,4), and C(4,0). What is its area?

Don"t be intimidated by the points. Graph them and find your base and height

This is easy because your base is just the distance from A to A on the horizontal plane, 8. The height is defined by the vertical distance of B, 4.

Your area is 16 sq. units.

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We know from the Co-ordinate Geometry, that, if the vertices of

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To find the area of triangle ABC with vertices A(-4,0), B(2,4), and C(4,0), you can use the formula for the area of a triangle given its vertices. One common method is using the formula:

[Area = \frac{1}{2} |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|]

Substituting the coordinates of points A, B, and C into this formula:

[Area = \frac{1}{2} |-4(4 - 0) + 2(0 - 4) + 4(4 - 0)|]

[= \frac{1}{2} |-16 + (-8) + 16|]

[= \frac{1}{2} |-16 - 8 + 16|]

[= \frac{1}{2} |-8|]

[= \frac{1}{2} \times 8]

[= 4]

Therefore, the area of triangle ABC is 4 square units.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- A chord with a length of #3 # runs from #pi/4 # to #pi/3 # radians on a circle. What is the area of the circle?
- A solid consists of a cone on top of a cylinder with a radius equal to that of the cone. The height of the cone is #9 # and the height of the cylinder is #12 #. If the volume of the solid is #36 pi#, what is the area of the base of the cylinder?
- Cups A and B are cone shaped and have heights of #24 cm# and #21 cm# and openings with radii of #8 cm# and #11 cm#, respectively. If cup B is full and its contents are poured into cup A, will cup A overflow? If not how high will cup A be filled?
- An ellipsoid has radii with lengths of #2 #, #5 #, and #4 #. A portion the size of a hemisphere with a radius of #3 # is removed form the ellipsoid. What is the remaining volume of the ellipsoid?
- Two corners of a triangle have angles of # (3 pi )/ 8 # and # ( pi ) / 6 #. If one side of the triangle has a length of # 14 #, what is the longest possible perimeter of the triangle?

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