QuestionFind the area of a scale drawing of a parallelogram where the scale is $10 \mathrm{~cm}$ for every $8 \mathrm{~m}$ on the sculpture. Base: $4.2 \mathrm{~m}$ , heights: $5 \mathrm{~m}$ and $6 \mathrm{~m}$ .

Studdy Solution

STEP 1

Assumptions1. The scale of the drawing is10 cm on the drawing for every8 m on the sculpture. . The base of the sculpture is4. m.
3. The heights of the sculpture are5 m and6 m.
4. The sculpture is a parallelogram, so the area is calculated as base times height.

STEP 2

First, we need to find the scale factor that converts measurements on the sculpture to measurements on the drawing. We can do this by dividing the measurement on the drawing by the measurement on the sculpture.
$Scale\, factor = \frac{Measurement\, on\, drawing}{Measurement\, on\, sculpture}$

STEP 3

Now, plug in the given values for the measurement on the drawing and the measurement on the sculpture to calculate the scale factor.
$Scale\, factor = \frac{10\, cm}{8\, m}$

STEP 4

Since1 m =100 cm, convert the measurement on the sculpture to cm.
$8\, m =800\, cm$ $Scale\, factor = \frac{10\, cm}{800\, cm}$

STEP 5

Calculate the scale factor.
$Scale\, factor = \frac{10}{800} =0.0125$

STEP 6

Now we need to calculate the scale measurements of the base and the heights of the sculpture using the scale factor. We can do this by multiplying the actual measurements by the scale factor.
$Scale\, measurement = Actual\, measurement \\times Scale\, factor$

STEP 7

Calculate the scale measurements for the base and the heights.
$Scale\, base =4.2\, m \\times0.0125 =0.0525\, cm$ $Scale\, height\,1 =5\, m \\times0.0125 =0.0625\, cm$ $Scale\, height\,2 =6\, m \\times0.0125 =0.075\, cm$

STEP 8

Now that we have the scale measurements, we can calculate the areas of the scale drawing for each height. The area of a parallelogram is base times height.
$Area = Base \\times Height$

STEP 9

Calculate the areas for each height.
$Area\, =.0525\, cm \\times.0625\, cm =.00328125\, cm^2$ $Area\,2 =.0525\, cm \\times.075\, cm =.0039375\, cm^2$ The areas of the scale drawing for the heights of5 m and6 m are.00328125 cm² and.0039375 cm² respectively.

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QuestionFind the area of a scale drawing of a parallelogram where the scale is $10 \mathrm{~cm}$ for every $8 \mathrm{~m}$ on the sculpture. Base: $4.2 \mathrm{~m}$ , heights: $5 \mathrm{~m}$ and $6 \mathrm{~m}$ .

Studdy Solution

STEP 1

Assumptions1. The scale of the drawing is10 cm on the drawing for every8 m on the sculpture. . The base of the sculpture is4. m.
3. The heights of the sculpture are5 m and6 m.
4. The sculpture is a parallelogram, so the area is calculated as base times height.

STEP 2

First, we need to find the scale factor that converts measurements on the sculpture to measurements on the drawing. We can do this by dividing the measurement on the drawing by the measurement on the sculpture.
$Scale\, factor = \frac{Measurement\, on\, drawing}{Measurement\, on\, sculpture}$

STEP 3

Now, plug in the given values for the measurement on the drawing and the measurement on the sculpture to calculate the scale factor.
$Scale\, factor = \frac{10\, cm}{8\, m}$

STEP 4

Since1 m =100 cm, convert the measurement on the sculpture to cm.
$8\, m =800\, cm$ $Scale\, factor = \frac{10\, cm}{800\, cm}$

STEP 5

Calculate the scale factor.
$Scale\, factor = \frac{10}{800} =0.0125$

STEP 6

Now we need to calculate the scale measurements of the base and the heights of the sculpture using the scale factor. We can do this by multiplying the actual measurements by the scale factor.
$Scale\, measurement = Actual\, measurement \\times Scale\, factor$

STEP 7

Calculate the scale measurements for the base and the heights.
$Scale\, base =4.2\, m \\times0.0125 =0.0525\, cm$ $Scale\, height\,1 =5\, m \\times0.0125 =0.0625\, cm$ $Scale\, height\,2 =6\, m \\times0.0125 =0.075\, cm$

STEP 8

Now that we have the scale measurements, we can calculate the areas of the scale drawing for each height. The area of a parallelogram is base times height.
$Area = Base \\times Height$

STEP 9

Calculate the areas for each height.
$Area\, =.0525\, cm \\times.0625\, cm =.00328125\, cm^2$ $Area\,2 =.0525\, cm \\times.075\, cm =.0039375\, cm^2$ The areas of the scale drawing for the heights of5 m and6 m are.00328125 cm² and.0039375 cm² respectively.

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QuestionFind the area of a scale drawing of a parallelogram where the scale is 10 cm10 \mathrm{~cm}10 cm for every 8 m8 \mathrm{~m}8 m on the sculpture. Base: 4.2 m4.2 \mathrm{~m}4.2 m, heights: 5 m5 \mathrm{~m}5 m and 6 m6 \mathrm{~m}6 m.

Studdy Solution

STEP 1

Assumptions1. The scale of the drawing is10 cm on the drawing for every8 m on the sculpture. . The base of the sculpture is4. m.3. The heights of the sculpture are5 m and6 m.4. The sculpture is a parallelogram, so the area is calculated as base times height.

STEP 2

STEP 3

Now, plug in the given values for the measurement on the drawing and the measurement on the sculpture to calculate the scale factor.Scale factor=10 cm8 mScale\, factor = \frac{10\, cm}{8\, m}Scalefactor=8m10cm​

STEP 4

Since1 m =100 cm, convert the measurement on the sculpture to cm.8 m=800 cm8\, m =800\, cm8m=800cmScale factor=10 cm800 cmScale\, factor = \frac{10\, cm}{800\, cm}Scalefactor=800cm10cm​

STEP 5

Calculate the scale factor.Scale factor=10800=0.0125Scale\, factor = \frac{10}{800} =0.0125Scalefactor=80010​=0.0125

STEP 6

STEP 7

STEP 8

Now that we have the scale measurements, we can calculate the areas of the scale drawing for each height. The area of a parallelogram is base times height.Area=BasetimesHeightArea = Base \\times HeightArea=BasetimesHeight

STEP 9

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QuestionFind the area of a scale drawing of a parallelogram where the scale is $10 \mathrm{~cm}$ for every $8 \mathrm{~m}$ on the sculpture. Base: $4.2 \mathrm{~m}$ , heights: $5 \mathrm{~m}$ and $6 \mathrm{~m}$ .

Assumptions1. The scale of the drawing is10 cm on the drawing for every8 m on the sculpture. . The base of the sculpture is4. m.
3. The heights of the sculpture are5 m and6 m.
4. The sculpture is a parallelogram, so the area is calculated as base times height.

Now, plug in the given values for the measurement on the drawing and the measurement on the sculpture to calculate the scale factor.
$Scale\, factor = \frac{10\, cm}{8\, m}$

Since1 m =100 cm, convert the measurement on the sculpture to cm.
$8\, m =800\, cm$ $Scale\, factor = \frac{10\, cm}{800\, cm}$

Calculate the scale factor.
$Scale\, factor = \frac{10}{800} =0.0125$

Now that we have the scale measurements, we can calculate the areas of the scale drawing for each height. The area of a parallelogram is base times height.
$Area = Base \\times Height$