Question

area of composite figures - set 3
find the area of the composite figure.
area of composite figures - set 3
find the area of the composite figure.
area of composite figures - set 3
find the area of the composite figure.
area of composite figures - set 3
find the area of the composite figure.

Explanation:

Step1: Analyze figure A

Divide figure A into rectangles. One rectangle has dimensions 8 x 6, another has dimensions (8 + 7) x (15 - 6), and the third has dimensions 4 x 9.

Step2: Calculate areas of rectangles in A

Area of first rectangle in A: $8\times6 = 48$. Area of second rectangle in A: $(8 + 7)\times(15 - 6)=15\times9 = 135$. Area of third rectangle in A: $4\times9 = 36$.

Step3: Sum areas of rectangles in A

Total area of figure A: $48+135 + 36=219$.

Step4: Analyze figure B

Divide figure B into rectangles. One rectangle has dimensions 16 x 5, another has dimensions (19 - 16) x (15 - 5), and the third has dimensions 5 x 3.

Step5: Calculate areas of rectangles in B

Area of first rectangle in B: $16\times5 = 80$. Area of second rectangle in B: $(19 - 16)\times(15 - 5)=3\times10 = 30$. Area of third rectangle in B: $5\times3 = 15$.

Step6: Sum areas of rectangles in B

Total area of figure B: $80+30 + 15=125$.

Step7: Analyze figure C

Divide figure C into rectangles. One rectangle has dimensions 9 x 7, another has dimensions (28 - 9) x 13, and the third has dimensions 14 x 7.

Step8: Calculate areas of rectangles in C

Area of first rectangle in C: $9\times7 = 63$. Area of second rectangle in C: $(28 - 9)\times13=19\times13 = 247$. Area of third rectangle in C: $14\times7 = 98$.

Step9: Sum areas of rectangles in C

Total area of figure C: $63+247+98 = 408$.

Step10: Analyze figure D

Divide figure D into rectangles. Consider the large rectangle with dimensions 12 x 9 and subtract the small rectangle with dimensions (12 - 6) x (9 - 2 - 2).

Step11: Calculate areas in D

Area of large rectangle in D: $12\times9 = 108$. Area of small rectangle in D: $(12 - 6)\times(9 - 2 - 2)=6\times5 = 30$.

Step12: Find area of figure D

Total area of figure D: $108-30 = 78$.

Answer:

Area of figure A: 219
Area of figure B: 125
Area of figure C: 408
Area of figure D: 78