Let y=4x^2 find the differential dy when x=5 and dx=0.4
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Answer:
- Driveway Area = 218 square feet
- Garden Area = 230 square feet
- Total Area = 448 square feet
See diagram below.
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Explanation:
Start at the lower left corner of the entire figure. Move 20 ft directly to the right until reach the end of the driveway at the bottom. Now move 10 ft up so you reach the other side of the driveway (the 26 ft side). In the process of moving 10 ft up, mark a new line segment. I've done so in red in the diagram below.
I've also drawn a green box. The red line and green box form a shape of a flag on a flagpole. The pole being 10 ft tall and the green box (flag) is a 6 by 3 rectangle. The 6 is from 26-20 = 6 and the 3 is from 10-7 = 3. Note how I'm subtracting the opposite side values to help figure out the dimensions of this green box.
The 10 ft by 20 ft portion of the driveway is 10*20 = 200 square feet. The green box adds on another 18 sq ft because 6*3 = 18. In all, we have 200+18 = 218 square feet for the driveway.
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If you want to know the area of the garden, then we first compute the overall area of everything shown. That's 32*14 = 448 square feet. Subtract off the driveway's area to get 448-218 = 230. Therefore, the garden's area is 230 square feet.
