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:

$\text{area}=\frac{1}{2}(base1+base2)\cdot\text{height}$

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:

$12\frac{3}{8}+12\frac{3}{8}=24\frac{6}{8}=24\frac{3}{4}=24.75in^2$

The area of the trapezoid is:

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

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:

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