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 enclosing rectangle area

The enclosing rectangle of triangle RST has length 8 and width 4. The area of a rectangle is $A = l\times w$, so the area of the rectangle is $8\times4$.

Step2: Subtract non - triangle areas

We can find the area of triangle RST by subtracting the areas of the non - triangle right - angled triangles within the rectangle from the area of the rectangle. The non - triangle right - angled triangles' areas can be combined and calculated. The correct way is to subtract the sum of the areas of the non - triangle right - angled triangles. The areas of these non - triangle right - angled triangles are half of the sum of the products of their bases and heights. The correct expression for subtracting the non - triangle areas is $\frac{1}{2}(10 + 12+16)$. So the area of triangle RST is $(8\times4)-\frac{1}{2}(10 + 12 + 16)$.

Answer:

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