Question

area of composite figures - set 1
find the area of the composite figure.
area of composite figures - set 2
find the area of the composite figure.
area of composite figures - set 1
find the area of the composite figure.
area of composite figures - set 2
find the area of the composite figure.

Explanation:

Step1: Analyze the first figure (I)

Divide it into two rectangles. One rectangle has dimensions 21×(30 - 19) and the other has dimensions 28×19.

Step2: Calculate the area of the first - part rectangle

The area of the rectangle with length 21 and width (30 - 19)=11 is $A_1=21\times11 = 231$.

Step3: Calculate the area of the second - part rectangle

The area of the rectangle with length 28 and width 19 is $A_2=28\times19=532$.

Step4: Calculate the total area of figure I

$A = A_1+A_2=231 + 532=763$.

Step5: Analyze the second figure (A)

Divide it into two rectangles. One rectangle has dimensions 13×(22 - 4) and the other has dimensions 28×4.

Step6: Calculate the area of the first - part rectangle

The area of the rectangle with length 13 and width (22 - 4)=18 is $A_3=13\times18 = 234$.

Step7: Calculate the area of the second - part rectangle

The area of the rectangle with length 28 and width 4 is $A_4=28\times4=112$.

Step8: Calculate the total area of figure A

$A'=A_3+A_4=234 + 112=346$.

Step9: Analyze the third figure (J)

Divide it into two rectangles. One rectangle has dimensions 21×(18 - 5) and the other has dimensions 14×5.

Step10: Calculate the area of the first - part rectangle

The area of the rectangle with length 21 and width (18 - 5)=13 is $A_5=21\times13 = 273$.

Step11: Calculate the area of the second - part rectangle

The area of the rectangle with length 14 and width 5 is $A_6=14\times5=70$.

Step12: Calculate the total area of figure J

$A''=A_5+A_6=273+70 = 343$.

Step13: Analyze the fourth figure (B)

Divide it into two rectangles. One rectangle has dimensions 20×(25 - 6) and the other has dimensions 13×6.

Step14: Calculate the area of the first - part rectangle

The area of the rectangle with length 20 and width (25 - 6)=19 is $A_7=20\times19 = 380$.

Step15: Calculate the area of the second - part rectangle

The area of the rectangle with length 13 and width 6 is $A_8=13\times6=78$.

Step16: Calculate the total area of figure B

$A'''=A_7+A_8=380 + 78=458$.

Answer:

I: 763
A: 346
J: 343
B: 458