Answer:
height = 4.8 cm
area = 120 cm²
perimeter = 62 cm
Step-by-step explanation:
**Please refer to the attached diagram when following the step-by-step**
First, find m∠C (green angle on diagram) by using the cosine rule:
[tex]c^2=a^2+b^2-2abcos(C)[/tex]
[tex]\implies 29^2=6^2+25^2-2(6)(25)cos(C)[/tex]
[tex]\implies cos(C)= \frac{29^2-6^2-25^2}{-2(6)(25)}[/tex]
[tex]\implies cos(C)= \frac{180}{-300}=-\frac{3}{5}[/tex]
[tex]\implies cos(C)=126.8698976... \textdegree[/tex]
Therefore, the interior angle of the right triangle at point C (blue angle on diagram) is:
[tex]180-cos^{-1}(-\frac{3}{5})=53.13010235... \textdegree[/tex]
Now use the Sine Rule (for finding sides) to determine height (h):
[tex]\frac{6}{sin(90)}=\frac{h}{sin(53.13..)}[/tex]
[tex]\implies \frac{6}{1}=\frac{h}{\frac{4}{5}}[/tex]
[tex]\implies 6 \times \frac{4}{5}=h[/tex]
[tex]\implies h=\frac{24}{5}=4.8[/tex]
So the height = 4.8 cm
Now we have determined the height, we can calculate the area by using the area of a parallelogram formula:
Area of a parallelogram = base x perpendicular height
⇒ area = 25 x 4.8 = 120 cm²
Parallelogram is a four-sided shape made up of two pairs of straight parallel lines that are equal in length.
Perimeter = sum of the sides
⇒ perimeter = 6 + 6 + 25 + 25 = 62 cm
