Question

consider a block of cheese cut in the shape of a Triangular prism. The front and back faces are isosceles triangles with a base 10 cm and a height of 12cm. The surface area of the block of cheese is 384 cm²

Answer 1

step 1

Find the thickness of the cheese

so

we know that

the surface area is the area of its two triangular faces plues the area of its three rectangular faces

so

Find the hypotenuse of the isosceles triangle

c^2=5^2+12^2

c^2=25+144

c^2=169

c=13

therefore

SA=2[(1/2)(10(12)]+2[(13)(h)]+10(h)

where

h is the thicknees

SA=384

substitute

384=2[(1/2)(10(12)]+2[(13)(h)]+10(h)

384=120+26h+10h

36h=384-120

36h=264

h=7.33 cm

so

statement A is false

step 2

Find the surface area of the front face

Find the area of the triangular isosceles face

so

A=(1/2)(10(12)

A=60 cm^2

so

statement B is false

step 3

the area of the front face is equal to the area of the back face

so

statement C is false

step 4

The area of the side faces and base is equal to

384-60=324 cm^2

statement D is false

step 5

the longer edhe of each triangular prism side is 13

the statement is true (see step 1)

answer is

the longer edhe of each triangular prism side is 13