The base b of the triangle is 11 cm.
To find the base b of the triangle, we need to compare its area with the area of the trapezoid.
The formula for the area of a triangle is 1/2 × base × height, while the formula for the area of a trapezoid is (1/2) × (sum of parallel sides) × height.
Since the two shapes have the same area, we can set up the following equation:
1/2 × b × 7 = (1/2) × (10 + 12) × 7
Simplifying the equation, we have:
1/2 × b × 7 = (1/2) × 22 × 7
Now, we can solve for b:
b = (1/2) × 22
b = 11 cm
The probable question may be:
The triangle and the trapezoid have the same area. What is the base b of the triangle?
The triangle ABC has Angle ABC=90 degree, AB=7 cm, BC=b.
The trapezoid MNPQ has 2 sides 10cm and 12cm and height is 7 cm