Question

What is the lateral area of the drawing?


A. 425 km2
B. 1021 km2
C. 200 km2
D. 114 km2

Answer 1

Each side is an isosceles trapezoid, so ED=2 since you would need to add 2 to each end of the bottom line to get the top line. Now use Pythagorean Theorem to get ED^2+AD^2=AE^2. Plug in your numbers to solve for AE. This is the height of each trapezoid. Then use your formula for the area of a trapezoid, (B1+B2)h/2, to get the area of each side, then multiply by 4 to get the lateral area since there are 4 sides. Remember lateral area is just the sides, then surface area is when you include the area of the two bases. 

Answer 2

Answer:  Option 'D' is correct.

Step-by-step explanation:

Since we have given 4 trapeziums with parallel sides :

$a=8\ km\\b=4\ km$

For height 'h'. we will consider the right angled triangle with

Perpendicular = 4.3 km and base = 2 km ,

We need to find the hypotenuse:

$H^2=B^2+P^2\\\\H^2=2^2+4.3^2\\\\H^2=4+18.49\\\\H=\sqrt{22.49}\\\\H=4.742\ km$

Now, Lateral surface area of the figure = 4 × Area of trapezium

$4\times \frac{1}{2}\times (8+4)\times 4.742\\\\=113.81\ km^2\\\\=114\ km^2$

Hence, Option 'D' is correct.