Question

The base of a triangle is $16$ inches and its altitude is $10$ inches. The area of the trapezoid cut off by a line $4$ inches from the vertex is

• A. $134.4$
• B. $67.2$
• C. $38.6$
• D. $72$
• E. not determined from the information given

Answer 1

Answer: (B)

$67.2$

The area of triangle is $\frac{1}{2}\times 16\times 10=80$
now a line cuts the triangle at $4$ inches from vertex, let the length of segment intersected by a line and triangle be $x$.
By similarity between two triangles, we get $\frac{x}{16}=\frac{4}{10}$, which gives $x=6.4$
So, the area of smaller triangle is $\frac{1}{2}\times 4\times 6.4=12.8$.
So, the area of trapezoid is $80-12.8=67.2$.