1. what is the area of the triangle? \n2. what is the reciprocal of $\frac{8}{11}$? \n3. $(\frac{1}{4})(\frac…

Explanation:

Step1: Recall triangle area formula

The formula for the area of a triangle is $A=\frac{1}{2}bh$. Since no base and height are given for the triangle in the problem, we assume this is an error and move on to solvable problems.

Step2: Find reciprocal

The reciprocal of a fraction $\frac{a}{b}$ is $\frac{b}{a}$. For $\frac{8}{11}$, the reciprocal is $\frac{11}{8}$.

Step3: Multiply fractions

To multiply $\frac{1}{4}\times\frac{1}{3}$, multiply the numerators and denominators. So $\frac{1\times1}{4\times3}=\frac{1}{12}$.

Step4: Identify division expression

The expression for 8 divided by a number $n$ is $\frac{8}{n}$, so the answer is d.

Step5: Calculate square - root

If $a = 25$, then $\sqrt{a}=\sqrt{25}=5$.

Step6: Calculate perimeter of trapezoid

The perimeter of a trapezoid is the sum of its side - lengths. For the trapezoid with side - lengths 8, 5, 10, 5, the perimeter $P=8 + 5+10 + 5=28$ cm.

Step7: Name the shape

The shape in question 6 is a trapezoid.

Step8: Calculate the mean

The mean of a set of numbers $x_1,x_2,\cdots,x_n$ is $\bar{x}=\frac{x_1 + x_2+\cdots+x_n}{n}$. For 2, 5, 11, $n = 3$, and $\bar{x}=\frac{2 + 5+11}{3}=\frac{18}{3}=6$.

Step9: Calculate the product

The product of 4 and 9 is $4\times9 = 36$.

Step10: Divide by 100

To divide 43.2 by 100, move the decimal point two places to the left. So $43.2\div100 = 0.432$.

Answer:

1. No solution (missing base and height)
2. $\frac{11}{8}$
3. $\frac{1}{12}$
4. d. $\frac{8}{n}$
5. 5
6. 28 cm
7. Trapezoid
8. 6
9. 36
10. 0.432