Question

Can you please help me out with a question

Answer 1

the figure is composed by a 4 triangles and a cube

to find the area of a triangle we need the base and height. the base is 15ft

to find the height we mut use the pithagorean theorem

h= height of the traingle

`h^2=(15ft)^2+(7.5ft)^2`

resolving we have

`h=\sqrt[\square]{281.25}\text{ = 16.78 aprox}`

and now he have all the measures

each triangle at the top has an area equal to

`A=(16.78ft\cdot15ft)/(2)=127.78sq\text{ ft}`

now we multiply that by 4: 127.78sq ft*4=503.1 sq ft

for the bottom part, there are 5 squares of side 15ft

each square has an area = 15ft*15ft = 225 sq ft

multipliying that by 5: 225sqft*5=1125 sq ft

the total area is 1125 sq ft+503.1sqft=1628.1 sq ft rounded is 1628 sq ft

For the volume of the piramid, we use

`V=(1)/(3)A\cdot h`

where A is the area of the base and h is the height

so volume of piramid:

`V=(1)/(3)\cdot225\text{sqft}\cdot15ft=1125ft^3`

for the volume of the cube we multiply the side length 3 times:

`V\mleft(cube\mright)=(15ft)^3=3375ft^3`

Adding the two volumes:

1125ft^3+3375ft^3=4500 cubic feet