The triangle and the trapezoid have the same area. Base b2 is twice the length of base b1. What are the lengths of the bases of the trapezoid?
What do you do after you find the area of the triangle?
Triangle: base=21 cm, height=6cm
Trapezoid: height=6 cm, b1=?, b2=?
11 and 5
i have this for my kids homework and we don't get it
5=b1 11=b2
To find the lengths of the bases of the trapezoid, we need to use the given information that the triangle and the trapezoid have the same area.
First, let's find the area of the triangle. The area of a triangle is given by the formula:
Area = (base * height) / 2
Using the values given:
Base = 21 cm
Height = 6 cm
Plug in the values into the formula:
Area = (21 * 6) / 2
Area = 63 cm²
Now that we have the area of the triangle, we can use it to find the lengths of the bases of the trapezoid.
The formula to calculate the area of a trapezoid is:
Area = [(b1 + b2) * h] / 2
We know that the height of the trapezoid is 6 cm (given), and the area of the trapezoid is also 63 cm² (equal to the triangle). Let's substitute the values into the formula:
63 = [(b1 + b2) * 6] / 2
Now, we can simplify the equation:
63 * 2 = (b1 + b2) * 6
126 = 6b1 + 6b2
Since we know that b2 is twice the length of b1 (given in the problem statement), we can substitute b2 with 2b1:
126 = 6b1 + 6(2b1)
126 = 6b1 + 12b1
126 = 18b1
Now, we can solve for b1:
b1 = 126 / 18
b1 = 7 cm
Therefore, the length of base b1 of the trapezoid is 7 cm.
Since we know that b2 is twice the length of b1, we can calculate b2:
b2 = 2 * b1
b2 = 2 * 7
b2 = 14 cm
Thus, the lengths of the bases of the trapezoid are b1 = 7 cm and b2 = 14 cm.
Thank you but I am still a little bit confused could you please help me out a bit?
I don' get what b1 is! Help
I dont it either!!!
the area of the triangle is ... half the base, times the height
the area of the trapezoid is ... the average of the bases, times the height
[(b1 + b2) / 2] * 6 = 1/2 * 21 * 6 ... b1 + b2 = 21
b2 = 2 * b1