Question

The area of the base of the oblique pentagonal pyramid is 50 cm2 and the distance from the apex to the center of the pentagon is 6 cm. The measure of ∠ACB is 45°. The height, AB, is ____ cm. The volume of the pyramid is ____ cm3.

Answer 1

Answer:

$\text{Height is }6\sqrt2cm$

$\text{The volume is }100\sqrt2cm^3$    

Step-by-step explanation:

Given the area of the base of the oblique pentagonal pyramid is $50 cm^2$ and the distance from the apex to the center of the pentagon is 6 cm. The measure of ∠ACB is 45°.

we know that

ABC is a right triangle

∠ACB=45°

AC=hypotenuse------> 6 cm

$\sin 45^{\circ}=\frac{AB}{AC}$

$AB=AC\times \sin 45$

$AB=\frac{6}{\sqrt2}$

$AB=3\sqrt2$

$\text{Height is }6\sqrt2cm$

Now, volume of pyramid

$\text{Volume of the pyramid=}\frac{1}{3}\times \text{Area of the base}\times height$

Area of the base=50 cm²

$Height=6\sqrt2 cm$

so, $\text{volume of the pyramid=}\frac{1}{3}\times 50\times 6\sqrt2=100\sqrt2cm^3$

$\text{the volume is }100\sqrt2cm^3$

Answer 2

6cm
100cm^3
That's the answer