Question

lesson 1 | session 3
3 an artist makes a scale drawing of a parallelogram - shaped sculpture. the scale is 10 cm on the drawing for every 8 m on the sculpture. what is the area of the scale drawing? show your work.
solution

Explanation:

Step1: Find the scale factor for length

The scale is \(10\) cm on drawing for \(8\) m in real - life. First, convert \(8\) m to cm (\(1\) m \( = 100\) cm, so \(8\) m \(=8\times100 = 800\) cm). The scale factor \(k=\frac{10}{800}=\frac{1}{80}\).

Step2: Find the dimensions of the parallelogram on the drawing

Let the base \(b = 5\) m and height \(h = 4.2\) m. Convert base and height to cm: \(b = 5\times100=500\) cm, \(h = 4.2\times100 = 420\) cm.
The base on the drawing \(b_d=500\times\frac{1}{80}=\frac{500}{80}=\frac{25}{4}\) cm.
The height on the drawing \(h_d=420\times\frac{1}{80}=\frac{420}{80}=\frac{21}{4}\) cm.

Step3: Calculate the area of the parallelogram on the drawing

The area of a parallelogram \(A = b\times h\). So \(A_d=\frac{25}{4}\times\frac{21}{4}=\frac{525}{16}=32.8125\) \(cm^{2}\).

Answer:

The area of the scale drawing is \(32.8125\) \(cm^{2}\).