Question

Three squares have the dimensions indicated in the diagram The area of the quadrilateral ABCD is

• A. $\frac{21}{4}$
• B. $\frac{15}{4}$
• C. $\frac{42}{4}$
• D. data not sufficient

Answer 1

Answer: (A)

The area of the quadrilateral ABCD is given by Area of the bigger triangle - area of small triangle,

Area of the large triangle

$=\frac{1}{2}\times base\times height=\frac{1}{2}\times \frac{5}{2}\times (2+3)=\frac{25}{4}$,

The sides of the triangles are in proportion,

base$=2$, height $=\frac{2}{10}\times 5=1$,

Area of the small triangle $=\frac{1}{2}\times 2\times 1=1$

area of the quadrilateral ABCD $=\frac{25}{4}-1=\frac{21}{4}$