Question

use the rectangle to fhig to solve problems 8 through 10. you can double-click on the figure to mark it.8. true or false · diagonals fi and hg are congruent.9. the measure of fi is 5 cm, what is the length of hg?10. true or false · diagonals fi and hg bisect each other.11. true or false · m<fhi =90° and triangle fhi is a right triangle.12. what is the measure of side hi? show your work. help video for 12 and 13.13. what is the area of rectangle fhig? must show work for full credit.

Explanation:

Step1: Answer rectangle diagonal congruence

By the properties of a rectangle, all diagonals are congruent. So this statement is True.

Step2: Apply rectangle diagonal congruence

Since diagonals of a rectangle are congruent, if $FI=5$ cm, then $HG=FI$.
$HG=5$ cm

Step3: Answer rectangle diagonal bisection

By rectangle properties, diagonals bisect each other. So this statement is True.

Step4: Answer right angle in rectangle

All angles in a rectangle are right angles, so $\angle FHI=90^\circ$, making $\triangle FHI$ a right triangle. This statement is True.

Step5: Calculate side HI via Pythagoras

In right $\triangle FHI$, use Pythagorean theorem: $FI^2 = FH^2 + HI^2$.
$$HI=\sqrt{FI^2 - FH^2}=\sqrt{5^2 - 3^2}=\sqrt{25-9}=\sqrt{16}=4\text{ cm}$$

Step6: Calculate rectangle area

Area of rectangle = length $\times$ width = $FH \times HI$.
$$\text{Area}=3\times4=12\text{ cm}^2$$

Answer:

1. True
2. 5 cm
3. True
4. True
5. 4 cm
6. $12\text{ cm}^2$