MATH SOLVE

2 months ago

Q:
# What is the area of the trapezoid? Enter your answer in the box. in2 The figure shows a trapezoid. The parallel bases of the trapezoid are horizontal, and top base is shorter than the bottom base. Vertical line segments are drawn inside the trapezoid from the upper vertices perpendicular to the bottom base. These segments are each 18 inches and divide the trapezoid into two right triangles and a rectangle. The rectangle lies between the two triangles. The bases of the triangles and rectangle make up the bottom base of the trapezoid. The base of each triangle is 6 inches, and the base of the rectangle is 15 inches.

Accepted Solution

A:

1. The area of the trapezoid (At) is:

At=A1+A2

At is the area of the trapezoid.

A1 is the area of the right triangles.

A2 is the area of the rectangle.

2. You can find the area of the right triangles (A1) by applying the formula for calculate the area of a triangle and multiply it by 2, because both triangles have the same dimensions. Then:

A1=2(bxh/2)

b is the base (b=6 inches).

h is the height (h=18 inches).

A1=2(6 inchesx18 inches/2)

A1=2(108 inches²/2)

A1=108 inches²

3. Now, you must find the area of the rectangle by applying the following formula:

A2=bxh

b is the base of the rectangle (b=15 inches).

h is the height ot the rectangle (h=18 inches).

A2=(15 inches)(18 inches)

A2=270 inches²

4. Therefore, the area of the trapezoid (At) is:

At=A1+A2

At=108 inches²+270 inches²

At=378 inches²

At=A1+A2

At is the area of the trapezoid.

A1 is the area of the right triangles.

A2 is the area of the rectangle.

2. You can find the area of the right triangles (A1) by applying the formula for calculate the area of a triangle and multiply it by 2, because both triangles have the same dimensions. Then:

A1=2(bxh/2)

b is the base (b=6 inches).

h is the height (h=18 inches).

A1=2(6 inchesx18 inches/2)

A1=2(108 inches²/2)

A1=108 inches²

3. Now, you must find the area of the rectangle by applying the following formula:

A2=bxh

b is the base of the rectangle (b=15 inches).

h is the height ot the rectangle (h=18 inches).

A2=(15 inches)(18 inches)

A2=270 inches²

4. Therefore, the area of the trapezoid (At) is:

At=A1+A2

At=108 inches²+270 inches²

At=378 inches²