Question

which expression can be used to find the area of triangle rst? (8·4)-\\(\frac{1}{2}\\)(10 + 12 + 16) (8·4)-(10 + 12 + 16) (8·4)-\\(\frac{1}{2}\\)(5 + 6 + 8) (8·4)-(5·6·8)

Explanation:

Step1: Use the area - subtraction method

The area of the rectangle formed by the out - most points (with length \(8\) and width \(4\)) is \(A_{rect}=8\times4\).

Step2: Calculate the area of the three non - triangle parts

We can use the formula for the area of a triangle \(A = \frac{1}{2}bh\).
The three non - triangle parts (smaller triangles) have bases and heights that can be counted from the grid.
The sum of the areas of the three non - triangle parts is \(\frac{1}{2}(10 + 12+16)\) (by calculating the area of each small triangle: for example, if one triangle has base \(5\) and height \(4\) (\(A_1=\frac{1}{2}\times5\times4 = 10\)), another has base \(6\) and height \(4\) (\(A_2=\frac{1}{2}\times6\times4=12\)), and the third has base \(8\) and height \(4\) (\(A_3=\frac{1}{2}\times8\times4 = 16\))).
The area of \(\triangle RST\) is the area of the rectangle minus the sum of the areas of the three non - triangle parts.

Answer:

\((8\cdot4)-\frac{1}{2}(10 + 12 + 16)\)