Question

find the perimeter and area of the following: image of a parallelogram with base 20 m, height 9 m, and a 45° angle at the bottom left vertex perimeter = dashed box units area = dashed box units² multiple choice options: 24, 24.6, 31.2, 34.02, 36, ...

Explanation:

Step1: Calculate the side length

We use the right triangle with height 9 m and 45° angle. For a 45-45-90 triangle, $\sin(45^\circ)=\frac{\text{opposite}}{\text{hypotenuse}}$, so side length $s=\frac{9}{\sin(45^\circ)}=\frac{9}{\frac{\sqrt{2}}{2}}=9\sqrt{2}\approx12.73$ m.

Step2: Compute perimeter of parallelogram

Perimeter formula: $P=2(a+s)$, where $a=20$ m.
$P=2(20 + 9\sqrt{2})=40 + 18\sqrt{2}\approx40+25.46=65.46$
(Note: Using the given options, we recheck: $9\sqrt{2}\approx12.73$, $2*(20+12.73)=65.46$, but if we use the approximate value from options, the closest matching calculation shows $2*(20+12.71)=65.42$, and among the extended set, the perimeter is $40 + 18\sqrt{2}\approx65.46$; however, for area:)

Step3: Calculate area of parallelogram

Area formula: $A = \text{base} \times \text{height}$
$A=20\times9=180$ m²

(Note: Since some options are cut off, the exact perimeter is $40 + 18\sqrt{2}\approx65.46$ and area is 180. If we assume the full options include these, the correct values are:)

Answer:

Perimeter = $40 + 18\sqrt{2} \approx 65.46$ units
Area = $180$ units²