11. Keng creates a painting on a rectangular canvas with a width that is four inches longer
than the height, as shown in the diagram below.

L= h +4 and H = h


A. Write a polynomial expression, in simplified form, that represents the area of the
canvas.

Keng adds a 3-inch-wide frame around all sides of his canvas.

B. Write a polynomial expression, in simplified form, that represents the total area of the canvas and the frame.

Part A

-------------------

Explanation:

We multiply the length and height to get the area

area = (length)*(height)

area = (h+4)*(h)

area = h(h+4)

area = h^2 + 4h .... apply the distributive property

The units for the area are in square inches.

===========================================================

Part B

-------------------

Explanation:

If we add a 3 inch frame along the border, then we're adding two copies of 3 inches along the bottom side. The h+4 along the bottom updates to h+4+3+3 = h+10 along the bottom.

Similarly, along the vertical side we'd have the h go to h+3+3 = h+6

The old rectangle that was h by h+4 is now h+6 by h+10

Multiply these expressions to find the area

area = length*width

area = (h+6)(h+10)

area = x(h+10) ..... replace h+6 with x

area = xh + 10x .... distribute

area = h( x ) + 10( x )

area = h( h+6 ) + 10( h+6 ) .... plug in x = h+6

area = h^2+6h + 10h+60 .... distribute again twice more

area = h^2 + 16h + 60

You can also use the box method or the FOIL rule as alternative routes to find the area.

The units for the area are in square inches.

The area of the canvas without the frame is h² + 4h and with frame is h²+16h+60.

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.

Given that, Keng is painting on a rectangular canvas with a width that is four inches longer than the height,

w = h+4, height = h

Area = (length)x(height)

area = (h+4)x(h)

area = h(h+4)

area = h² + 4h

With the frame,

If we add a 3 inch frame along the border, then we're adding two copies of 3 inches along the bottom side. The h+4 along the bottom updates to h+4+3+3 = h+10 along the bottom.

Keng added a 3-inch-wide frame around the painting,

Therefore,

The h+4 will become h+4+3+3 = h+10

Similarly, along the vertical side = h+3+3 = h+6

Area = (h+10)(h+6) = h²+16h+60

Hence, the area of the canvas without the frame is h² + 4h and with frame is h²+16h+60.

Learn more about areas, click;

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