Answer:
Step-by-step explanation:
Area Of Triangle And Rectangle
Given a triangle of base b and height h (perpendicular to b), the area can be computed by
[tex]\displaystyle A=\frac{bh}{2}[/tex]
A rectangle of the same dimensions has an area of
[tex]A=bh[/tex]
We have a triangle of base 3 cm and a height of 4 cm. Its area is
[tex]\displaystyle A=\frac{(3)(4)}{2}=6\ cm^2[/tex]
That triangle moves upward at 4 cm per second for 3 seconds. It means that the triangle 'sweeps' upwards three times its height forming a rectangle of base 3 cm and height 12 cm. The area of the swept area is
[tex]A=(3)(12)=36\ cm^2[/tex]
The triangle stays in the top of this rectangle, so its area is part of the total swept area:
Total swept area = 6 + 36 = [tex]42\ cm^2[/tex]
