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: Find the area of the rectangle

The rectangle has length \(8\) and width \(4\), so its area is \(8\times4\).

Step2: Use the formula for the area of a triangle

The area of triangle \(RST\) can be found by subtracting the sum of the areas of three right - angled triangles from the area of the rectangle.
The areas of the three right - angled triangles are \(\frac{1}{2}\times(5\times2)\), \(\frac{1}{2}\times(6\times1)\) and \(\frac{1}{2}\times(8\times1)\).
The sum of their areas is \(\frac{1}{2}(5\times2 + 6\times1+8\times1)=\frac{1}{2}(10 + 12+16)\)

Answer:

\((8\times4)-\frac{1}{2}(10 + 12+16)\)