Question

Using a simulator at space​ camp, you practice landing your individual spaceship on landing platforms that have different shapes. The score you get depends on the area of the platform. To find the area of this​ platform, divide it into a triangle and a parallelogram. Then find the area of each part and add.

A five-sided shape has a horizontal bottom of length 6 meters. The sides that extend from the bottom of the shape are parallel, the same length, and rise from left to right. The remaining sides extend from the upper ends of the parallel sides to form a vertex. The perpendicular distance from the base to this vertex is 7 meters. The perpendicular distance from the base to the upper left vertex is 4 meters.

Answer 1

The Area of the platform is 33m²

Explanation:

As the question says, the height of vertex from the base (D from AB) is 7m whereas the height of left vertex from the base (E from AB) is 4m

Thus it means the height of the Δ DCE (DX)= 7-4 ⇒3m

Since the platform is five-sided, the figure can be broken down into constituting parts

1. Parallelogram ║ABCE
2. Δ DCE

Are of the figure= Area of ║ABCE+ area Δ DCE

Area of ║ABCE= breadth * height

= 6*4 ⇒24m ²

Area Δ DCE= ½*(base)(height)

Putting the value of base is 6m and height as 3m

Area Δ DCE= ½*6*3

=9m ²

Total area= 24+9= 33m ²