To find the area of the shaded region, you must find the area of the larger rectangle [(x+10)×(2x+5)] and subtract the area of the smaller rectangle [(x+1)×(x+1)] from it.

First, you simplify the larger rectangle's area:

(x+10)×(2x+5) = $2x^{2} +25x+50$

Then, simplify the smaller rectangle's area:

(x+1)×(x+1) = $x^{2} +2x+1$

Finally, subtract the smaller rectangle's area from the larger rectangle's area:

$(2x^{2} +25x+50) - (x^{2} +2x+1) = x^{2} +23x+49$

Therefore, the final answer is $x^{2} +23x+49$ .

I hope this helps!

8 0

2 years ago

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the area of a rectangular pyramid is 65yd^2. the length of the playground is 3 yards longer than twice it's width. find the leng

schepotkina [342]

The area formula for a rectangle = Length x Width
Let length = L and width = W.
We also know that the length is 3 yards longer than twice it's width.
SO this means L = 3 PLUS 2 times W
L = 3 + 2W
Now plug that into the area formula and we get:
Area = (3 + 2W) x W
You'll need to multiply everything in the brackets by W.
So what would (3 + 2W)x W = ?

4 0

3 years ago