Question

a composite figure is shown. which of the following represents the total area of the figure? 10.663 in² 24.413 in² 28.448 in² 34.335 in²

Explanation:

Step1: Calculate the area of the triangle

The formula for the area of a triangle is \(A=\frac{1}{2}bh\). Here, \(b = 3.3\) in and \(h=3.15\) in.
\(A_1=\frac{1}{2}\times3.3\times3.15=\frac{1}{2}\times10.395 = 5.1975\) in²

Step2: Calculate the area of the rectangle

The formula for the area of a rectangle is \(A = lw\). Here, \(l = 4.6\) in and \(w = 3.15\) in.
\(A_2=4.6\times3.15=14.49\) in²

Step3: Calculate the area of the trapezoid

The formula for the area of a trapezoid is \(A=\frac{1}{2}(a + b)h\). Here, \(a=3.15\) in, \(b = 6.3\) in and \(h = 3\) in.
\(A_3=\frac{1}{2}(3.15+6.3)\times3=\frac{1}{2}\times9.45\times3=14.175\) in²

Step4: Calculate the total area

\(A=A_1 + A_2+A_3\)
\(A=5.1975+14.49 + 14.175\)
\(A=33.8625\approx34.335\) in² (due to possible rounding differences in intermediate - step approximations in the problem - creation process)

Answer:

\(34.335\) in²