Question

The surface area of this pyramid is 189 cm The area of the square base is 49 cm . What is the area of one triangular face of the lateral surface? Show the steps of your solution and explain your work.

Answer 1

Well, the area of the pyramid is = (area of the base) + 4 x (area of a triangular face)

Now, given that, can you solve your problem?

Answer 2

so 49 + 4 and idk the are of the triangular face thats what its asking for

Answer 3

Call the area of a triangular face to be x.

Then you know that
189 = 49 + 4x

Can you now find x?

Answer 4

i can divide 189 by 49 to find x , correct ?

Answer 5

No. Think this through. The total surface area (SA) of the pyramid is 189 cm^2. The SA of the square is 49 cm^2. What must be the total surface area of the four triangles?

Answer 6

196 ..?

Answer 7

Total SA of the 4 triangles = SA of Pyramid - SA of square
= 189 - 49
= 140

Yes?

Answer 8

Alright i got that , now what ? what do i do to find x ?

Answer 9

The area of the 4 triangles is 140 cm^2. Hence what is the area of one of the triangles?

Answer 10

the area of one of the triangles is 49 ?

Answer 11

No. If 4 times the area of a triangle is 140, what is the area of that triangle?

Answer 12

35 ?

Answer 13

Yes

Answer 14

140/4 = 35

Answer 15

so is that my answer ?

Answer 16

Alternatively, let x be the area of a triangle. As they are all the same and
SA Pyramid = SA Square + 4(SA Triangle),
we must have that
189 = 49 + 4x

Hence

4x = 189 - 49
= 140

thus
x = 140 / 4
= 35

Yes, 35 cm^2 is the area of a triangle.

Make sure you understand the logic of it.

Answer 17

OMG , thanks so much ! I will be writing this down (:

Answer 18

OMG thank u