Question

calculate the slant height for the given square pyramid.
Round to the nearest tenth.

Pyramid base= 6cm
height=5 cm


6.2 cm
5.8 cm
7.8 cm
7.2 cm





Calculate the length of the diagonal for the given rectangular prism.
Round to the nearest tenth.

Length= 10 cm
widith= 4cm
height= 10cm


14.7 cm
10.8 cm
12.2 cm
15.6 cm


Calculate the length of the diagonal for the given rectangular prism.
Round to the nearest tenth.

Length= 14cm
widith= 3
height= 4 cm

Answer 1

First, we will calculate the slant height for the square pyramid:

To solve this, we can use the Pythagorean Theorem (a^2 + b^2 = c^2).
In this case, a is half the base (3 cm) and b is the height (5 cm).

3^2 + 5^2 = c^2
9 + 25 = c^2
34 = c^2
c = √34
c ≈ 5.8 cm

So, the slant height of the pyramid is approximately 5.8 cm.

Next, we will calculate the length of the diagonal for the first rectangular prism:

To solve this, we can use the 3D Pythagorean Theorem (a^2 + b^2 + c^2 = d^2).
In this case, a is the length (10 cm), b is the width (4 cm), and c is the height (10 cm).

10^2 + 4^2 + 10^2 = d^2
100 + 16 + 100 = d^2
216 = d^2
d = √216
d ≈ 14.7 cm

So, the length of the diagonal for the first rectangular prism is approximately 14.7 cm.

Finally, we will calculate the length of the diagonal for the second rectangular prism:

To solve this, we can use the 3D Pythagorean Theorem (a^2 + b^2 + c^2 = d^2) again.
In this case, a is the length (14 cm), b is the width (3 cm), and c is the height (4 cm).

14^2 + 3^2 + 4^2 = d^2
196 + 9 + 16 = d^2
221 = d^2
d = √221
d ≈ 14.9 cm

So, the length of the diagonal for the second rectangular prism is approximately 14.9 cm.