Question:
The diagram shows a right -angle and a parallelogram. The area of the parallelogram is 5 times the area of the triangle. The perpendicular height of the parallelogram is h. Find h
Answer:
[tex]h =12cm[/tex]
Step-by-step explanation:
Given
Triangle
[tex]Base = 9cm[/tex]
[tex]Height = 16cm[/tex]
Parallelogram
[tex]Base = 30cm[/tex]
[tex]Height = h[/tex]
Calculate the area of the triangle
[tex]Area = 0.5 * Base * Height[/tex]
[tex]Area = 0.5 * 9cm * 16cm[/tex]
[tex]Area = 72cm^2[/tex]
When multiplied by 5, gives the area of the parallelogram.
So:
The area of Parallelogram is:
[tex]Area = Base * Height[/tex]
[tex]Area = 30cm * h[/tex]
This gives:
[tex]30cm * h = 72cm^2 * 5[/tex]
Make h the subject
[tex]h = \frac{72cm^2 * 5}{30cm}[/tex]
[tex]h = \frac{72cm^2}{6cm}[/tex]
[tex]h =12cm[/tex]
