Question

Write an equation that represents the following situations. Then, solve the equations, 1) Heidi designs office furniture. Her latest project is a tabletop in the shape of a trapezoid with two rectangles cut out for a computer station. Each rectangle has an area of 12 in. The following is the design of the table. 28-1 in h - 8 in 10 in 10 in 16 17 in If Heidi needs to cover the desktop with a glass panel that also has the cutouts, what is the area of the glass panel? a. Write the equation in words. b. Calculate the two areas. 4 = c. Choose a variable for the unknown quantity and write the equation with the substituted values. d. Solve the equation. Include appropriate units in your answer.

Answer 1

h=8 in

Area of each rectangle = 12 and 3/8 squared inches.

a)The area of the glass panel is the area of the trapezoid minus the area of the rectangles. The area of a trapezoid is calculated as the following:

`\text{area}=(1)/(2)(base1+base2)\cdot\text{height}`

This is the height times 1/2 times the sum of the top edge plus the bottom edge

b)The area of the rectangles is the sum of both of them:

`12(3)/(8)+12(3)/(8)=24(6)/(8)=24(3)/(4)=24.75in^2`

The area of the trapezoid is:

`\text{area}=(1)/(2)\cdot(16.25+28.25)\cdot8=178in^2`

c) Let's say G is the area of the glass panel we must find, this equals to the area of the trapezoid minus the area of the rectangles:

`G=178-24.75`

d) G is then:

`G=178-24.75=153.25in^2`