Question

area of composite figures - set 3
find the area of the composite figure.
9
5
6 8
23
area of composite figures - set 3
find the area of the composite figure.
17
11
2
7 12
10
24

Explanation:

Step1: Analyze the first composite - figure

The large rectangle has length \(l = 23\) and width \(w\) which can be found by adding the vertical lengths: \(9 + 5=14\). The area of the large rectangle \(A_{1}=23\times14 = 322\). The small rectangle to be subtracted has length \(l_{s}=8\) and width \(w_{s}=5\), so its area \(A_{s}=8\times5 = 40\).

Step2: Calculate the area of the first composite - figure

The area of the first composite figure \(A = A_{1}-A_{s}=322 - 40=282\).

Step3: Analyze the second composite - figure

The large rectangle has length \(l = 24\) and width \(w = 10 + 11=21\). The area of the large rectangle \(A_{1}=24\times21 = 504\). The first small rectangle to be subtracted has length \(l_{s1}=7\) and width \(w_{s1}=11\), so its area \(A_{s1}=7\times11 = 77\). The second small rectangle to be subtracted has length \(l_{s2}=12\) and width \(w_{s2}=2\), so its area \(A_{s2}=12\times2 = 24\).

Step4: Calculate the area of the second composite - figure

The area of the second composite figure \(A=A_{1}-A_{s1}-A_{s2}=504-(77 + 24)=504 - 101 = 403\).

Answer:

First figure: 282
Second figure: 403