Question

find the area of the figure. enter the correct number in the box. show hints units²

Explanation:

Step1: Enclose in a rectangle

Enclose the figure in a rectangle with vertices \((-5,4)\), \((5,4)\), \((5, - 4)\) and \((-5,-4)\). The length of the rectangle's sides are \(10\) (horizontal) and \(8\) (vertical), so the area of the rectangle \(A_{rect}=10\times8 = 80\).

Step2: Subtract areas of surrounding triangles

There are 4 surrounding right - angled triangles.

• Triangle 1: With base \(6\) and height \(2\), area \(A_1=\frac{1}{2}\times6\times2 = 6\).
• Triangle 2: With base \(4\) and height \(2\), area \(A_2=\frac{1}{2}\times4\times2=4\).
• Triangle 3: With base \(6\) and height \(2\), area \(A_3=\frac{1}{2}\times6\times2 = 6\).
• Triangle 4: With base \(4\) and height \(2\), area \(A_4=\frac{1}{2}\times4\times2=4\).

The total area of the 4 triangles is \(A_{triangles}=A_1 + A_2+A_3+A_4=6 + 4+6 + 4=20\).

Step3: Calculate area of the figure

The area of the figure \(A = A_{rect}-A_{triangles}=80 - 20=30\).

Answer:

30