Question

question 8
what is the area of the rhombus shown below?
$ac=17$
$bd=15$
a. 16 square units
b. 127.5 square units
c. 255 square units
d. 190.4 square units

question 9
if the area of the trapezoid below is 98 square units, what is the value of $x$?
a. 1.75 units
b. 7 units
c. 3.5 units
d. 14 units

question 10
which expression gives the perimeter of the regular heptagon shown below?
a. $7x$
b. $x+7$
c. $\frac{x}{7}$
d. $x^7$

Explanation:

Question 8

Step1: Recall rhombus area formula

The area of a rhombus is $\frac{1}{2} \times d_1 \times d_2$, where $d_1$ and $d_2$ are the lengths of its diagonals.

Step2: Substitute given diagonal values

Here, $d_1=AC=17$, $d_2=BD=15$. Substitute into the formula:
$\text{Area} = \frac{1}{2} \times 17 \times 15$

Step3: Calculate the result

$\frac{1}{2} \times 255 = 127.5$

Step1: Recall trapezoid area formula

The area of a trapezoid is $\frac{1}{2} \times (b_1 + b_2) \times h$, where $b_1, b_2$ are the bases, $h$ is the height.

Step2: Substitute known values

Given $\text{Area}=98$, $b_1=8$, $b_2=20$, $h=x$. Substitute:
$98 = \frac{1}{2} \times (8 + 20) \times x$

Step3: Simplify and solve for x

First calculate the sum of bases: $8+20=28$. Then:
$98 = \frac{1}{2} \times 28 \times x$
$98 = 14x$
$x = \frac{98}{14} = 7$

Step1: Recall regular polygon perimeter rule

A regular heptagon has 7 equal sides of length $x$. Perimeter is the sum of all sides.

Step2: Calculate perimeter expression

Perimeter = $x + x + x + x + x + x + x = 7x$

Answer:

B. 127.5 square units

---

Question 9