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McGraw Hill Glencoe Geometry, 2012

MH

McGraw Hill Glencoe Geometry, 2012 View details

6. Two-Dimensional Figures

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Exercise 53 Page 64

The frame and the painting together form a rectangle. The difference between the area of this rectangle and the area of the painting is the area of the frame.

We will use the formula that expresses the area of a rectangle in terms of its length

ℓ

and width

w .

A = ℓ w

The Area of the Frame and Painting Together

The width of the frame is added to both sides of the painting, so to find the width of the framed painting we add

2

inches twice to the given width of the painting.

w = 2 + 18 + 2 = 22 inches

To get the height of the framed painting, we need to add the width of the frame twice to the given height of the painting. This is what we will consider the length of the rectangle.

ℓ = 2 + 14 + 2 = 18 inches

We now have all measurements to find the area of the framed painting.

A = ℓ w

$ℓ = 18$ , $w = 22$

A = (18) (22)

Multiply

A = 396

The Area of the Painting

To find the area of the painting, we use the given width,

w = 18,

and height,

ℓ = 14 .

A_{p} = ℓ w

$ℓ = 14$ , $w = 18$

A_{p} = (14) (18)

Multiply

A_{p} = 252

The Area of the Frame

The difference between the area of the framed painting and the area of the painting alone is the area of the frame.

A_{f} = A - A_{p}

$A = 396$ , $A_{p} = 252$

A_{f} = 396 - 252

Subtract term

A_{f} = 144

The area of the frame is

144 in^{2},

so the correct answer is C.

Alternative Solution

Alternative way of thinking

Instead of finding the area of the frame as a difference, we can think of the frame as put together using rectangles.

We can now find the area of the individual rectangles.

Color	Size	Number	Total area
Red	$2 \times 2 = 4$	$4$	$4 \cdot 4 = 16$
Blue	$18 \times 2 = 36$	$2$	$2 \cdot 36 = 72$
Green	$2 \times 14 = 28$	$2$	$2 \cdot 28 = 56$

The area of the frame is the sum of these areas.

A_{f} = 16 + 72 + 56 = 144 in^{2}

Subchapter links

Check Your Understanding p.61

Practice and Problem Solving p.61-63

H.O.T. Problems p.63

Standardized Test Practice p.64

Spiral Review p.64

Skills Review p.64