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Sagot :
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
[tex]h^2=(15ft)^2+(7.5ft)^2[/tex]resolving we have
[tex]h=\sqrt[\square]{281.25}\text{ = 16.78 aprox}[/tex]and now he have all the measures
each triangle at the top has an area equal to
[tex]A=\frac{16.78ft\cdot15ft}{2}=127.78sq\text{ ft}[/tex]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
[tex]V=\frac{1}{3}A\cdot h[/tex]where A is the area of the base and h is the height
so volume of piramid:
[tex]V=\frac{1}{3}\cdot225\text{sqft}\cdot15ft=1125ft^3[/tex]for the volume of the cube we multiply the side length 3 times:
[tex]V\mleft(cube\mright)=(15ft)^3=3375ft^3[/tex]Adding the two volumes:
1125ft^3+3375ft^3=4500 cubic feet
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