Question

liam uses a scale factor of 3.5 to create a scale drawing of the triangle shown. find the area of liams scale drawing. square centimeters

Explanation:

Step1: Calculate the new base and height

When a figure is scaled by a scale factor \(k\), the new dimensions are \(k\) times the original dimensions.
The original base \(b = 4\space cm\) and original height \(h=7\space cm\). After scaling with \(k = 3.5\), the new base \(B=4\times3.5 = 14\space cm\) and new height \(H = 7\times3.5=24.5\space cm\).

Step2: Use the area formula for a triangle

The area formula for a triangle is \(A=\frac{1}{2}\times base\times height\).
Substitute \(B = 14\space cm\) and \(H=24.5\space cm\) into the formula: \(A=\frac{1}{2}\times14\times24.5\).
First, \(14\times24.5 = 343\). Then \(\frac{1}{2}\times343=171.5\).

Answer:

\(171.5\)