Question

A group of students made trees out of paper for a scene in a school play. The trees are shaped like square pyramids. 2 ft How much paper will it take to make each tree, including the bottom?

Answer 1

Answer:

Step-by-step explanation:

The area of a triangle is base*height/2

So one triangle is 2*4/2=4

Multiplied by 4 sides, 4*4=16

Finally the base is a square, so 2*2=4

Therefore the entire shape is 16+4=20 square feet

Answer 2

The amount of paper it will take to make each tree, including the bottom is 20 ft²

How to find the surface area of some object?

Find the area that its outer surfaces possess. Sum of all those surfaces' area is the surface area of the considered object.

Surface area of paper tree = sum of areas of those 4 slant standing triangles + area of base

Area of each of those 4 triangles are same (assuming they're symmetric).

Each triangle has height of 4 ft and base of 2 ft. (the base is a square of side length 2 ft).

Thus, we get:

Area of 4 triangles = 4(area of each tree ) = $4\left (\dfrac{1}{2} \times \text{base} \times \text{height}\right) = 4\left (\dfrac{1}{2} \times 2 \times 4\right) = 16 \: \rm ft^2$

Area of square base = $\text{side}^2 = 2^2 = 4 \: \rm ft^2$

Thus, we get:

Surface area of paper tree = 16 + 4 = 20 ft²

Thus, the amount of paper it will take to make each tree, including the bottom is  20 ft²

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