# Explain how the formula for the area of a trapezoid can be used to find the formulas for the areas of parallelograms and triangles?

Trapezoid has bases

Its area is

Parallelogram:

Triangle:

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The formula for the area of a trapezoid is A = (1/2)h(b1 + b2), where h is the height and b1 and b2 are the lengths of the two parallel sides (bases) of the trapezoid.

To find the formula for the area of a parallelogram, we can imagine splitting the parallelogram into two congruent triangles by drawing a diagonal. Each of these triangles is half of a trapezoid with bases equal to the sides of the parallelogram and height equal to the height of the parallelogram. Therefore, the area of each triangle is (1/2)h(b1 + b2), and since there are two triangles, the total area of the parallelogram is h(b1 + b2), which is the same as the formula for the area of a trapezoid when b1 = b2.

To find the formula for the area of a triangle, we can consider a triangle as a trapezoid with one of its bases having length 0. In this case, the formula for the area of the trapezoid simplifies to A = (1/2)hb, where h is the height of the triangle and b is the length of its base. This is the formula for the area of a triangle.

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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 triangle has two corners with angles of # pi / 6 # and # (5 pi )/ 8 #. If one side of the triangle has a length of #15 #, what is the largest possible area of the triangle?
- How do you use Heron's formula to find the area of a triangle with sides of lengths #7 #, #4 #, and #9 #?
- A chord with a length of #3 # runs from #pi/12 # to #pi/6 # radians on a circle. What is the area of the circle?
- Cups A and B are cone shaped and have heights of #25 cm# and #27 cm# and openings with radii of #12 cm# and #6 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?
- How do you find the area of a regular octagon given a radius?

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