Question

scare Drawings Wendell is designing the layout of the backyard behind his new home. He wants to build a dog house and add some flower gardens. In the following tasks, you will help Wendell create a scale drawing of his backyard to he him plan the location and size of the dog house and gardens. The provided sketch is not drawn to scale, but it does give the actual dimensions of the lawn in feet. The backyard is a trapezoid-the west side is perpendicula to both the north and south sides, and the deck is a rectangle. The scale factor of the drawing is 1 inch to 10 feetpart Bin the scale drawing, what will the length of the east side of the backyard be?part C in the scale drawing, what will the length of the south side of the backyard be?part Din the scale drawing, what will the length of the west side of the backyard be?part Ein the scale drawing, what will the length of the north side of the backyard be?part Ftwo corners of the backyard are right angles. the third corner forms an obtuse angle measuring 127°, the fourth corner forms an acute angle measuring 53°, when transferring these angle measurements from the real world to the scale drawing, will their measures increase, decrease, or stay the same?part G in the scale drawing, what is the area of the lawn (that is, the area of the whole backyard, except for the deck)?

Answer 1

Part B

scale factor is given as 1 inch to 10 feet

In the diagram, the actual length of the east side is 35 feet,

the length of the east side on the scale drawing will be 35/10 = 3.5 inches

Part C

In the diagram, the actual length of the south side is 71 feet,

the length of the south side on the scale drawing will be 71/10 = 7.1 inches

Part D

In the diagram, the actual length of the west side is 28 feet,

the length of the west side on the scale drawing will be 28/10 = 2.8 inches

Part E

In the diagram, the actual length of the north side is 50 feet,

the length of the north side on the scale drawing will be 50/10 = 5 inches

Part F

The measurement of the angles will stay the same on the scale drawing

Part G

The whole backyard is a trapezoid while the deck is a rectangle

so,

area of the lawn = Area of Backyard (trapezoid) - area of lawn (rectangle)

Area of backyard =

`\begin{gathered} (1)/(2)(a\text{ + b)h} \\ =(1)/(2)(5\text{ + 7.1)2.8} \\ =(1)/(2)(12.1)2.8=16.94inch^2\text{ } \end{gathered}`

Area of deck = length x breadth

`1*0.5=0.5inch^2`

Area of the lawn =

`16.94inch^2-0.5inch^2=16.44inch^2`