A square pyramid is divided in the middle by a square. The top smaller shaded pyramid has a side length of 10cm and the bottom larger shaded pyramid has a side length of 15cm.
For the square pyramid, find:
1. The ratio of the smaller shaded area to the larger shaded area.
2. The size of the smaller area, given that the larger area is 400cm².
1. The ratio of the smaller shaded area to the larger shaded area can be determined by calculating the ratio of the square of their side lengths.
Let x be the side length of the smaller square, and y be the side length of the larger square. We are given x = 10cm and y = 15cm.
The ratio of the smaller area to the larger area is (x^2) / (y^2) = (10^2) / (15^2) = 100 / 225 = 4/9.
So, the ratio of the smaller shaded area to the larger shaded area is 4:9.
2. Given that the larger shaded area is 400 cm², we can calculate the size of the smaller shaded area using the ratio we found above.
Let A1 be the area of the smaller shaded pyramid and A2 be the area of the larger shaded pyramid. We know that A2 = 400 cm².
We can set up the proportion (A1 / A2) = (x^2 / y^2) = (10^2 / 15^2) = 4/9.
Substitute A2 = 400 cm² and solve for A1:
A1 / (400) = 4 / 9
A1 = (4/9) * 400
A1 = 177.78 cm²
Therefore, the size of the smaller shaded area is approximately 177.78 cm².