Question

The whole surface of a trapezoid-shaped carpet needs to be covered with an outer rag. Find the total area of the rag used to cover the carpet given in the figure below.

• A. 56 sq in
• B. 153 sq in
• C. 70.5 sq in
• D. 76.5 sq in

Answer 1

The correct option is D 76.5 sq in

Area of the trapezoid PQRSTU = Area of the $\Delta PUT$ + Area of the rectangle PQST + Area of the $\Delta QSR$
Area of the $\Delta \text{PUT}=\frac{1}{2}\times$ base $\times$ height
$=\frac{1}{2}\times UT\times PT$
$=\frac{1}{2}\times 4\times 9$
= 18 sq in

Area of the rectangle PQST = Length $\times$ Width
$=PQ\times QS$
$=5\times 9=45\text{sq in}$

Area of the $\Delta QSR=\frac{1}{2}\times$ base $\times$ height
Base of the $\Delta QSR,SR=UR-(UT+TS)$
$=12-(4+5)$
= 12 − 9 = 3 in
Area of the $\Delta QSR=\frac{1}{2}\times SR\times QS$
$=\frac{1}{2}\times 3\times 9$
$=13.5\text{sq in}$

Area of the trapezoid PQRSTU = 18 + 45 + 13.5
= 76.5 sq in

Alternative formula to calculate the area of the trapezoid: $\frac{1}{2}\times$ (sum of parallel sides)$\times$ height
Area of the trapezoid PQRSTU $=\frac{1}{2}\times (UR+PQ)\times QS$
$=\frac{1}{2}\times (12+5)\times 9$
$=\frac{1}{2}\times 17\times 9=76.5\text{sq in}$
Option B is correct