Question

what is the area of this figure?
write your answer using decimals, if necessary.
square millimeters

Explanation:

Step1: Calculate the area of the triangle

The formula for the area of a triangle is \(A=\frac{1}{2}\times base\times height\). Here, the base of the triangle is \(5\) mm and the height is \(2\) mm. So, \(A_{triangle}=\frac{1}{2}\times5\times2 = 5\) \(mm^{2}\)

Step2: Calculate the area of the large rectangle

The length of the large rectangle: \(10-(6 - 4)=8\) mm, and the width is \(7\) mm. Using the formula \(A = length\times width\), \(A_{large - rectangle}=8\times7=56\) \(mm^{2}\)

Step3: Calculate the area of the small rectangle

The length is \(4\) mm and the width is \(2\) mm. Using the formula \(A = length\times width\), \(A_{small - rectangle}=4\times2 = 8\) \(mm^{2}\)

Step4: Sum up the areas

\(A=A_{triangle}+A_{large - rectangle}+A_{small - rectangle}\)
\(A=5 + 56+8=69\) \(mm^{2}\)

Answer:

\(69\)