Chapter 11.3, Problem 15PSC

To determine

To Calculate: Area of the original triangle.

Answer to Problem 15PSC

The area of the original triangle is $16$ square units.

Explanation of Solution

Given information:

The area of the trapezoid is $12$ square units.

  

Calculation:

Here, $\Delta ADB,\Delta DBE$ and $\Delta BEC$ are isosceles and have equal areas.

And, Area of trapezoid = $12$

So, area of each triangle = $\frac{12}{3}=4$

And, original triangle contains $4$ of smaller triangles

(three in trapezoid and one overlapping from folding)

So that, area of original isosceles triangle = $4\times 4=16$

Conclusion: Hence,the area of the original triangle is $16$