Final answer:
To find the area of a trapezoid, we use the formula: Area = (base1 + base2) ÷ 2 × height. In this case, the bases are AD and BC and the height is AB. To find the area of CAD, we treat it as a separate triangle and use the formula: Area = (base × height) ÷ 2.
Step-by-step explanation:
The area of CAD in a trapezoid ABCD is given as 23 dm^2. We need to determine the option that represents this area. To find the area of a trapezoid, we use the formula: Area = (base1 + base2) ÷ 2 × height. In this case, the bases are AD and BC and the height is AB. Since we are looking for the area of CAD, we can treat triangle CAD as a separate triangle. We know the area of CAD is 23 dm^2, so we can calculate the base and height of CAD using the formula: Area = (base × height) ÷ 2. Solving for base, we multiply both sides by 2 and divide by the height: base = (2 × Area) ÷ height. Substituting the values, we get base = (2 × 23) ÷ AB. Now, we can substitute the base into the formula to find the area of the trapezoid: Area = (AD + BC) ÷ 2 × AB. We can substitute base for AD and solve for BC using the base formula: BC = base - AD. Finally, we substitute the values into the area formula: Area = (base + (base - AD)) ÷ 2 × AB. Evaluating this expression will give us the option representing the area of CAD.