Question

which expressions represent the area of the triangle in square feet? select all that apply. a $\frac{1}{2}cdot48cdot9$ b $\frac{1}{2}(6 + 8)(9)$ c $(14cdot9)div2$ d $\frac{1}{2}(6)(9)+\frac{1}{2}(8)(9)$ e $(6)(9)+(8)(9)div2$

Explanation:

Step1: Recall triangle - area formula

The area formula for a triangle is $A=\frac{1}{2}bh$, where $b$ is the base and $h$ is the height. The base of the given triangle is $6 + 8=14$ feet and the height is 9 feet.

Step2: Calculate area using formula

$A=\frac{1}{2}(6 + 8)\times9=\frac{1}{2}\times14\times9=(14\times9)\div2$. Also, we can consider the triangle as composed of two non - overlapping right - triangles with bases 6 and 8 and the same height 9. Then the area $A=\frac{1}{2}(6)\times9+\frac{1}{2}(8)\times9$.

Step3: Analyze each option

• Option A: $\frac{1}{2}\times48\times9$, since $48

eq14$, this is incorrect.

• Option B: $\frac{1}{2}(6 + 8)\times9$, correct as per the formula.
• Option C: $(14\times9)\div2$, correct as it is equivalent to $\frac{1}{2}\times14\times9$.
• Option D: $\frac{1}{2}(6)\times9+\frac{1}{2}(8)\times9$, correct as per the non - overlapping right - triangle approach.
• Option E: $(6\times9)+(8\times9)\div2$ is incorrect.

Answer:

B. $\frac{1}{2}(6 + 8)(9)$
C. $(14\times9)\div2$
D. $\frac{1}{2}(6)(9)+\frac{1}{2}(8)(9)$