17 7.G.A.1 Math.7.G.1 7.G.A.1 7.G.1 7.G.1 CC.2.3.7.A.2 M07.C-G.1.1.1 MA.7.GR.1.5 7.PAR.4.6 7.GM.6

Scale Drawings 7th Grade

Alabama Course of Study Standards: 17
Solve problems involving scale drawings of geometric figures, including computation of actual lengths and areas from a scale drawing and reproduction of a scale drawing at a different scale.
Arizona Academic Standards: 7.G.A.1
Solve problems involving scale drawings of geometric figures, such as computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.
Common Core State Standards: Math.7.G.1 or 7.G.A.1
Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.
North Carolina - Standard Course of Study: 7.G.1
Solve problems involving scale drawings of geometric figures by: Building an understanding that angle measures remain the same and side lengths are proportional. Using a scale factor to compute actual lengths and areas from a scale drawing. Creating a scale drawing.
Ohio's Learning Standards: 7.G.1
Solve problems involving similar figures with right triangles, other triangles, and special quadrilaterals. Compute actual lengths and areas from a scale drawing and reproduce a scale drawing at a different scale. Represent proportional relationships within and between similar figures.
Pennsylvania Core Standards: CC.2.3.7.A.2
Visualize and represent geometric figures and describe the relationships between them.
Pennsylvania Core Standards: M07.C-G.1.1.1
Solve problems involving scale drawings of geometric figures, including finding length and area.
Florida - Benchmarks for Excellent Student Thinking: MA.7.GR.1.5
Solve mathematical and real-world problems involving dimensions and areas of geometric figures, including scale drawings and scale factors.
Georgia Standards of Excellence (GSE): 7.PAR.4.6
Solve everyday problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.
Arkansas Academic Standards: 7.GM.6
Calculate the scale factor, compute the actual lengths from the scale in a drawing, and reproduce a scale drawing using another scale.

If the scale factor from figure A to figure B is k,
then the area of figure B is k^² times the area of figure A.

Figure 1 has side lengths: a, b, and c.
A scale factor of k has been applied to figure 1 to produce figure 2.
So, figure 2 has side lengths: k times a, k times b, and k times c.

The area of a triangle is one-half times the base times the height.
Examine the areas of both figures.

Area_{_{figure 1}}	=	$\frac{1}{2}$ ab
Area_{_{figure 2}}	=	$\frac{1}{2}$ (ka)(kb)
	=	kk( $\frac{1}{2}$ ab)
	=	k^²(Area_{_{figure 1}})

So, the area of figure 2 is k^² times the area of figure 1.

A scale drawing (or scale model) is a proportional representation of an object.

A scale drawing's scale indicates the relationship between the
representation's measurements and the actual measurements.

\begin{array}{rcl} \frac{1 in.}{14.4 ft} & = & \frac{5 in.}{x} \\ 1 in. (x) & = & 5 in. (14.4 ft) \\ 1 in. (x) & = & 72 in. ft \\ 1 in. (x) \div 1 in. & = & 72 in. ft \div 1 in. \\ x & = & 72 ft \end{array}

Area	=	base × height
	=	$\frac{5}{8}$ in. × $1 \frac{1}{4}$ in.
	=	$\frac{5}{8}$ in. × $\frac{5}{4}$ in.
	=	$\frac{25}{32}$ sq in.

The scale for area is the scale for length squared.
So, the scale for area is 1 square inch to (14.4)^² square feet, which is 1 square inch to 207.36 square feet.
To find the area in square feet, multiply

\frac{25}{32}

square inch by 207.36 sq ft/sq in.

207.36 sq ft/sq in. ×

\frac{25}{32}

sq in. = 162 sq ft

Scale Drawings

Alabama Course of Study Standards: 17

Solve problems involving scale drawings of geometric figures, including computation of actual lengths and areas from a scale drawing and reproduction of a scale drawing at a different scale.

Arizona Academic Standards: 7.G.A.1

Solve problems involving scale drawings of geometric figures, such as computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

Common Core State Standards: Math.7.G.1 or 7.G.A.1

Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

North Carolina - Standard Course of Study: 7.G.1

Solve problems involving scale drawings of geometric figures by:
Building an understanding that angle measures remain the same and side lengths are proportional.
Using a scale factor to compute actual lengths and areas from a scale drawing.
Creating a scale drawing.

Ohio's Learning Standards: 7.G.1

Solve problems involving similar figures with right triangles, other triangles, and special quadrilaterals.
Compute actual lengths and areas from a scale drawing and reproduce a scale drawing at a different scale.
Represent proportional relationships within and between similar figures.

Pennsylvania Core Standards: CC.2.3.7.A.2

Visualize and represent geometric figures and describe the relationships between them.

Pennsylvania Core Standards: M07.C-G.1.1.1

Solve problems involving scale drawings of geometric figures, including finding length and area.

Florida - Benchmarks for Excellent Student Thinking: MA.7.GR.1.5

Solve mathematical and real-world problems involving dimensions and areas of geometric figures, including scale drawings and scale factors.

Georgia Standards of Excellence (GSE): 7.PAR.4.6

Solve everyday problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

Arkansas Academic Standards: 7.GM.6

Calculate the scale factor, compute the actual lengths from the scale in a drawing, and reproduce a scale drawing using another scale.

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