Question

area of triangles and parallelograms
which expression can be used to find the area of triangle rst?
(8 - 4)-(5 - 6 - 8)
(8 - 4)-\frac{1}{2}(10 + 12 + 16)
(8 - 4)-\frac{1}{2}(3 + 6 + 8)
(8 - 4)+(10 + 12 + 16)

Explanation:

Step1: Recall area formula for triangle

The area of a triangle can be found by enclosing it in a rectangle and subtracting the areas of the surrounding right - angled triangles.

Step2: Enclose triangle RST in a rectangle

If we enclose $\triangle RST$ in a rectangle with vertices that enclose the triangle, assume the rectangle has an area that can be calculated as the product of its length and width. Let's assume the rectangle has dimensions such that its area is $8\times4$.

Step3: Calculate areas of surrounding right - angled triangles

We need to find the areas of the right - angled triangles around $\triangle RST$. The sum of the areas of these right - angled triangles is $\frac{1}{2}(10 + 12+16)$.

Step4: Find area of $\triangle RST$

The area of $\triangle RST$ is the area of the enclosing rectangle minus the sum of the areas of the surrounding right - angled triangles, which is $(8\times4)-\frac{1}{2}(10 + 12+16)$.

Answer:

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