# Explain how the formula for the area of a trapezoid is derived from the formula for the area of a triangle?

Trapezoid can be divided into two triangles by a diagonal. These triangles will have bases that correspond to trapezoid's bases and altitudes equal to trapezoid's altitude.

One of the way to explain a formula for an area of a trapezoid using a formula for a triangle can be as follows.

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The formula for the area of a trapezoid can be derived from the formula for the area of a triangle by considering the trapezoid as the difference between two triangles. The area of a triangle is given by the formula A = 1/2 * base * height.

In a trapezoid, if we extend the two non-parallel sides to meet at a point, we create two triangles and a rectangle. The area of the trapezoid is the sum of the areas of these two triangles minus the area of the rectangle.

The formula for the area of a trapezoid, therefore, can be expressed as: A = (1/2 * base1 * height) + (1/2 * base2 * height) - (base2 - base1) * height.

Simplifying this expression yields the formula for the area of a trapezoid: A = (1/2) * (base1 + base2) * height.

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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.

- Two corners of an isosceles triangle are at #(6 ,4 )# and #(9 ,2 )#. If the triangle's area is #36 #, what are the lengths of the triangle's sides?
- Two corners of a triangle have angles of #(3 pi ) / 4 # and # pi / 6 #. If one side of the triangle has a length of #5 #, what is the longest possible perimeter of the triangle?
- A isosceles triangular prism has a height of #15 cm#, the perimeter of the base is #32 cm# and the base of the triangle is #6/5# the side. Calculate the surface area of the prism?
- 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 #33 # and the height of the cylinder is #17 #. If the volume of the solid is #84 pi#, what is the area of the base of the cylinder?
- A pyramid has a parallelogram shaped base and a peak directly above its center. Its base's sides have lengths of #2 # and #9 # and the pyramid's height is #6 #. If one of the base's corners has an angle of #pi/4 #, what is the pyramid's surface area?

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