The question is not written properly! Complete question along with answer and explanation is provided below.
Question:
Farrah is making a dragon costume for her little brother. It would have triangular spikes down the head and back.
Each head spike has a base of 2 cm and a height of 6 cm.
Each back spike will be 10 cm high with a base of 6 cm.
if the costume has 6 spikes on the back and on the head 10 more spikes than the back then how many square centimeters of fabric will farrah need for all the dragon spikes?
Given Information:
Base of head spike = b₁ = 2 cm
Height of head spike = h₁ = 6 cm
Base of back spike = b₂ = 6 cm
Height of back spike = h₂ = 10 cm
Number of head spikes = n₁ = 10 + 6 = 16
Number of back spikes = n₂ = 6
Required Information:
How much fabric is needed = ?
Answer:
Farrah would need 276 cm² of fabric for all the dragon spikes.
Step-by-step explanation:
We are given that dragon costume have triangular spikes down the head and back.
The area of triangular shape is given by
Area = ½×b×h
Where b is the base and h is the height
The area of the head spike is
A₁ = ½×b₁×h₁
A₁ = ½×2×6
A₁ = ½×12
A₁ = 6 cm²
But we know that the number of head spikes is 16 so the total area of the head spikes is
A₁ = 16×6
A₁ = 96 cm²
The area of the back spike is
A₂ = ½×b₂×h₂
A₂ = ½×6×10
A₂ = ½×60
A₂ = 30 cm²
But we know that the number of back spikes is 6 so the total area of the back spikes is
A₂ = 6×30
A₂ = 180 cm²
The total area required is the sum of the area of head spikes and back spikes,
Total area = A₁ + A₂
Total area = 96 + 180
Total area = 276 cm²
Therefore, Farrah would need 276 cm² of fabric for all the dragon spikes.
