Question

samantha is cutting fabric pieces to make patches for her jacket. in order to know how much thread will be required for the stitching, she first needs to know the perimeter of the piece. calculate the perimeter of the piece as shown. enter the unknown segment length(s), then calculate the perimeter of the polygon. perimeter of the quadrilateral: centimeters

Explanation:

Step1: Identify known side lengths

We have the lengths of three sides: \( 13 \), \( 2.83 \) (wait, no, looking at the graph, the horizontal segment from \( D(5,7) \) to \( (8,7) \)? Wait, no, the coordinates: \( R(-7,2) \), \( D(5,7) \) (wait, the label says \( D(5, 7) \) and another point \( (8,7) \)? Wait, the sides: \( R \) to \( D \) is \( 13 \), \( D \) to the next point (let's call it \( Q(8,7) \)): horizontal distance, so \( 8 - 5 = 3 \) (wait, the graph grid: each square is 1 unit? Wait, the coordinates: \( R(-7,2) \), \( W(1,-3) \), \( D(5,7) \), and \( Q(8,7) \)? Wait, the given lengths: \( R \) to \( D \): \( 13 \), \( D \) to \( Q \): let's calculate the horizontal distance between \( (5,7) \) and \( (8,7) \): \( 8 - 5 = 3 \) cm. \( Q \) to \( W \): length \( 12.21 \), \( W \) to \( R \): \( 9.43 \). Wait, no, the quadrilateral is \( R \), \( D \), \( Q \), \( W \), back to \( R \)? Wait, the sides are \( RD = 13 \), \( DQ = 3 \) (since \( x \) from 5 to 8, \( y \) same 7, so distance \( |8 - 5| = 3 \)), \( QW = 12.21 \), \( WR = 9.43 \).

Step2: Sum all side lengths

Perimeter \( = 13 + 3 + 12.21 + 9.43 \)
First, \( 13 + 3 = 16 \)
Then, \( 12.21 + 9.43 = 21.64 \)
Then, \( 16 + 21.64 = 37.64 \)? Wait, no, wait the coordinates: let's recheck. Wait, \( D \) is \( (5,7) \), the next point is \( (8,7) \), so distance is \( 8 - 5 = 3 \) (since \( y \) is same, horizontal line). Then \( Q(8,7) \) to \( W(1,-3) \): let's calculate that distance. Wait, maybe I misread the length. Wait the graph has \( 12.21 \) as the length from \( Q \) to \( W \)? Wait, the given lengths: \( R \) to \( D \): \( 13 \), \( D \) to \( Q \): let's see the grid. From \( x=5 \) to \( x=8 \), that's 3 units (each grid square is 1 unit, since the x-axis goes from -8 to 9, each tick is 1). So \( DQ = 3 \). Then \( QW \): the length given is \( 12.21 \), \( WR \): \( 9.43 \), \( RD \): \( 13 \). So perimeter is \( 13 + 3 + 12.21 + 9.43 \). Let's calculate:

\( 13 + 3 = 16 \)

\( 12.21 + 9.43 = 21.64 \)

\( 16 + 21.64 = 37.64 \)? Wait, but maybe the horizontal segment is \( 2.83 \)? No, wait \( x \) from 5 to 8 is 3. Wait, maybe the coordinates are \( D(5,7) \) and \( Q(7,7) \)? Wait, the label says \( D(5, 7) \) and \( (8,7) \)? Wait, the original problem's graph: let's check the coordinates again. \( R(-7,2) \), \( W(1,-3) \), \( D(5,7) \), and \( (8,7) \). So the sides are \( R-D \) (13), \( D-(8,7) \) (distance 3), \( (8,7)-W \) (12.21), \( W-R \) (9.43). So sum all: \( 13 + 3 + 12.21 + 9.43 = 37.64 \). Wait, but maybe I made a mistake. Wait, let's recalculate the perimeter by adding all the given side lengths: 13, 2.83 (wait, no, the horizontal segment: from \( x=5 \) to \( x=8 \), that's 3 units. Wait, maybe the length is 3 (since 8-5=3). Then 13 + 3 + 12.21 + 9.43 = 37.64. Alternatively, maybe the horizontal segment is 2.83? Wait, no, 8-5=3. So the perimeter is 13 + 3 + 12.21 + 9.43 = 37.64. Wait, but let's check the numbers again. 13 + 3 is 16, 12.21 + 9.43 is 21.64, 16 + 21.64 is 37.64. So the perimeter is 37.64? Wait, but maybe the horizontal segment is 2.83? Wait, maybe the coordinates are \( D(5,7) \) and \( Q(7,7) \), so 7-5=2, but no, the label says \( (8,7) \). Wait, the original problem's graph: the point after D is (8,7), so x from 5 to 8 is 3. So I think the perimeter is 13 + 3 + 12.21 + 9.43 = 37.64. Wait, but maybe the horizontal length is 2.83? Wait, no, 8-5=3. So I think the answer is 37.64. Wait, but let's check the sum again: 13 + 3 = 16; 12.21 + 9.43 = 21.64; 16 + 21.64 = 37.64. So the perimeter is 37.64 centimeters.

Answer:

37.64