SOLUTION: MATHEMATICS-GRADE 10 ASSIGNMENT a brick-walled,fixed dog kennel in the form of a 15-units by 20-units by 10-units rectangular prism was built ,the roof was just a rectangular

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Question 953652: MATHEMATICS-GRADE 10 ASSIGNMENT

a brick-walled,fixed dog kennel in the form of a 15-units by 20-units by 10-units rectangular prism was built ,the roof was just a rectangular concrete slab.a 2units square entrance space was opened in the on the longer surface of the kennel. due to limited space at the compound ,pyramidal-wooden pigeon hall units high was built on top of the kennel. calculate the outer surface area of the rectangular kennel
calculate the outer surface area of the pyramidal pigeonhole
total surface area of the whole structure
calculate the volume of the whole structure
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
a brick-walled,fixed dog kennel in the form of a
W=15-units by L=20-units by h=10-units rectangular prism was built ,
the roof was just a rectangular concrete slab=>W=15-units by L=20
all together is a rectangular prism, and the total surface area is:
SA+=+2+LW++%2B++2+Lh++%2B++2Wh+
SA+=+2+%2A20%2A15++%2B++2+%2A20%2A10++%2B++2%2A15%2A10+
SA+=+600+%2B++400++%2B++300+
SA+=+1300+


a=2units square entrance space was opened in the on the longer surface of the kennel
a%5E2=4units square entrance that should be deducted from the surface area of the rectangular prism
SA-a%5E2+=+1300-4=+1296 the surface area of the rectangular kennel

due to limited space at the compound , pyramidal-wooden pigeon hall units high was built on top of the kennel
A rectangular pyramid is made up of 1 rectangular base and 4 triangles going up from the base to the top of the pyramid.
The surface area is the area of all five parts added together.

in your case 1 rectangular base is already part of surface area of the rectangular kennel, so we need only SA%5Bp%5D of 4 triangles ,
note that 2 of them have base length 20 units and 2 of them have base length of 15 units
so, we need higth (I do not see it is given for the pyramidal pigeonhole)
2%2A%281%2F2%29L%2Ah and 2%2A%281%2F2%29W%2Ah
SA%5Bp%5D=2%2A%281%2F2%2920%2Ah%2B2%2A%281%2F2%2915%2Ah
SA%5Bp%5D=20%2Ah%2B15%2Ah
SA%5Bp%5D=35%2Ah
so, to calculate the outer surface area of the pyramidal pigeonhole we need h and I can just do it using same higth as given for kennel h=10
SA%5Bp%5D=35%2A10
SA%5Bp%5D=350
total surface area of the whole structure:
SA%2BSA%5Bp%5D=1296%2B350
SA%2BSA%5Bp%5D=1646 squared units
calculate the volume of the whole structure:
V%5Bk%5D%2BV%5Bp%5D=20%2A15%2A10%2B%281%2F3%2920%2A15%2A10
V%5Bk%5D%2BV%5Bp%5D=3000%2B%281%2F3%293000
V%5Bk%5D%2BV%5Bp%5D=4000 cubic units