The front view of a piece of art is in the shape of a rhombus. The front view of the art has diagonals that are 1.4 yards long and 0.8 yard long. What is the area of the front view of the piece of art?

14in
8.6 in

1 answer

To find the area of a rhombus when the lengths of its diagonals are known, you can use the formula:

\[ \text{Area} = \frac{d_1 \times d_2}{2} \]

where \( d_1 \) and \( d_2 \) are the lengths of the diagonals.

In this case, the diagonals are given as:

  • \( d_1 = 1.4 \) yards
  • \( d_2 = 0.8 \) yards

Now, plug in the values into the formula:

\[ \text{Area} = \frac{1.4 \times 0.8}{2} \]

Calculating \( 1.4 \times 0.8 \):

\[ 1.4 \times 0.8 = 1.12 \]

Now, divide by 2:

\[ \text{Area} = \frac{1.12}{2} = 0.56 \text{ square yards} \]

To convert square yards to square inches, remember that \(1 \text{ yard} = 36 \text{ inches}\). Therefore, \(1 \text{ square yard} = 36^2 \text{ square inches} = 1296 \text{ square inches}\).

Now convert the area to square inches:

\[ 0.56 \text{ square yards} \times 1296 \text{ square inches/square yard} = 726.72 \text{ square inches} \]

Thus, the area of the front view of the piece of art is approximately \(726.72\) square inches.