Question

Laisha drew a model on grid paper of a decorator tile that she wants to buy. Each grid line represents 5 cm. Her drawing has coordinates (3, 4), (5, 10), (7, 4), and (5, 0). Calculate the area of the real tile

Answer 1

500 cm²

Explanation:

The diagonals of this kite figure are perpendicular, so the area is given by ...

A = (1/2)(d1)(d2)

where d1 and d2 are the diagonal lengths.

The horizontal diagonal extends from x=3 to x=7, so is 4 units, 20 cm, long.

The vertical diagonal extends from y=0 to y=10, so is 10 units, 50 cm long.

The area is ...

A = (1/2)(20 cm)(50 cm) = 500 cm²

The area of Laisha's tile is 500 cm².