Question

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

Explanation:

Step1: Analyze figure E

Split figure E into two rectangles. One rectangle has dimensions 24 by 14, and the other has dimensions 12 by 5.

Step2: Calculate area of first rectangle in E

The area formula for a rectangle is $A = l\times w$. For the first rectangle in E with $l = 24$ and $w=14$, $A_1=24\times14 = 336$.

Step3: Calculate area of second rectangle in E

For the second rectangle in E with $l = 12$ and $w = 5$, $A_2=12\times5=60$.

Step4: Find total area of figure E

$A_E=A_1 + A_2=336+60 = 396$.

Step5: Analyze figure G

Split figure G into two rectangles. One rectangle has dimensions 24 by 8, and the other has dimensions $(21 - 8)$ by 12.

Step6: Calculate area of first rectangle in G

For the first rectangle in G with $l = 24$ and $w = 8$, $A_3=24\times8 = 192$.

Step7: Calculate area of second rectangle in G

The length of the second - rectangle in G is $21 - 8=13$, and width is 12. So $A_4=13\times12 = 156$.

Step8: Find total area of figure G

$A_G=A_3+A_4=192 + 156=348$.

Step9: Analyze figure F

Split figure F into two rectangles. One rectangle has dimensions 15 by 6, and the other has dimensions 21 by 13.

Step10: Calculate area of first rectangle in F

For the first rectangle in F with $l = 15$ and $w = 6$, $A_5=15\times6=90$.

Step11: Calculate area of second rectangle in F

For the second rectangle in F with $l = 21$ and $w = 13$, $A_6=21\times13 = 273$.

Step12: Find total area of figure F

$A_F=A_5+A_6=90 + 273=363$.

Step13: Analyze figure H

Split figure H into two rectangles. One rectangle has dimensions 22 by 6, and the other has dimensions 22 by $(33 - 6)$.

Step14: Calculate area of first rectangle in H

For the first rectangle in H with $l = 22$ and $w = 6$, $A_7=22\times6=132$.

Step15: Calculate area of second rectangle in H

The length of the second rectangle in H is 22, and width is $33 - 6 = 27$. So $A_8=22\times27=594$.

Step16: Find total area of figure H

$A_H=A_7+A_8=132 + 594=726$.

Answer:

E: 396
G: 348
F: 363
H: 726