a triangular road sign has a height of 8 feet and a base of 16.5 feet. How much larger in area is this sign than one with a height of 4 feet and a base of 8.25 feet?
Please fully explain how you got this cause i'm really confused!!!
since the sides of the two similar road signs are in the ratio of 2 : 1
so their areas are proportional to the square of their sides
2^2 : 1^2 = 4 : 1
so the second is 4 times larger.
You could do it the long way, and actually calculate their areas. You will find the the first answer is 4 times the second answer.
Triangle area:
A = bh/2
A = (16.5 * 8)/2
A = 132/2
A = 66 square feet
Find the area of the smaller triangle the same way.
thank you Reiny and Ms. Sue!! I wouldn't be able to make it through my math class without you!
You're welcome, Audrey.
To find the difference in area between the two triangular road signs, we need to calculate the area of each sign separately and then compare the results.
The formula for the area of a triangle is:
Area = (base * height) / 2
Let's calculate the area of each sign step by step.
For the first sign with a height of 8 feet and a base of 16.5 feet:
Area1 = (base1 * height1) / 2
= (16.5 * 8) / 2
= 66
So, the area of the first sign is 66 square feet.
Now, let's calculate the area of the second sign with a height of 4 feet and a base of 8.25 feet:
Area2 = (base2 * height2) / 2
= (8.25 * 4) / 2
= 16.5
So, the area of the second sign is 16.5 square feet.
To find the difference in area, we subtract the area of the second sign from the area of the first sign:
Difference in area = Area1 - Area2
= 66 - 16.5
= 49.5 square feet
Therefore, the triangular road sign with a height of 8 feet and a base of 16.5 feet is 49.5 square feet larger in area than the sign with a height of 4 feet and a base of 8.25 feet.