Question

aaron drew the figure below for a school art project. what is the total area of the figure? use the drop - down menus to complete the sentences to determine the total area of the figure. click the arrows to choose an answer from each menu. the trapezoid has a height of 3 inches, a shorter base measuring choose... inches, and a longer base measuring choose... inches. the total area of the entire figure is choose... square inches.

Explanation:

Step1: Identify the shapes and their dimensions

The figure consists of a rectangle on the left with length $4$ inches and width $2.75$ inches, a trapezoid in the middle with height $3$ inches, a shorter - base of $2.75$ inches (same as the width of the left - hand rectangle) and a longer base of $4.25$ inches, a rectangle in the middle - right with length $3$ inches and width $3$ inches, and a triangle on the right with base $3$ inches and height $2.5$ inches.

Step2: Calculate the area of the first rectangle

The area formula for a rectangle is $A = lw$. For the first rectangle with $l = 4$ inches and $w = 2.75$ inches, $A_1=4\times2.75 = 11$ square inches.

Step3: Calculate the area of the trapezoid

The area formula for a trapezoid is $A=\frac{(b_1 + b_2)h}{2}$, where $b_1 = 2.75$ inches, $b_2 = 4.25$ inches and $h = 3$ inches. So $A_2=\frac{(2.75 + 4.25)\times3}{2}=\frac{7\times3}{2}=10.5$ square inches.

Step4: Calculate the area of the second rectangle

For the second rectangle with $l = 3$ inches and $w = 3$ inches, $A_3=3\times3 = 9$ square inches.

Step5: Calculate the area of the triangle

The area formula for a triangle is $A=\frac{1}{2}bh$, where $b = 3$ inches and $h = 2.5$ inches. So $A_4=\frac{1}{2}\times3\times2.5 = 3.75$ square inches.

Step6: Calculate the total area

The total area $A = A_1+A_2+A_3+A_4=11 + 10.5+9+3.75=34.25$ square inches.

Answer:

$34.25$