Question

Victoria drew a square with an area of 20 1/4 square inches a rectangle with an area of 20 5/6 squares inches and a triangle with an area of 20.4 square inches pick all the true statements A The triangle area is neither the smallest nor the largest B the rectangle has the largest area C the square area is larger than the rectangle area D The triangle area smaller than the square area

Answer 1

To evaluate the areas, let's first convert all the areas into improper fractions or decimal form for easier comparison:

1. **Square Area**:
\[
20 \frac{1}{4} = 20 + \frac{1}{4} = \frac{80}{4} + \frac{1}{4} = \frac{81}{4} \text{ square inches}
\]
Converting to decimal:
\[
\frac{81}{4} = 20.25 \text{ square inches}
\]

2. **Rectangle Area**:
\[
20 \frac{5}{6} = 20 + \frac{5}{6} = \frac{120}{6} + \frac{5}{6} = \frac{125}{6} \text{ square inches}
\]
Converting to decimal:
\[
\frac{125}{6} \approx 20.8333 \text{ square inches}
\]

3. **Triangle Area**:
\[
20.4 \text{ square inches}
\]
This is already in decimal form.

Now, let's compare the areas:

- **Square**: 20.25 square inches
- **Rectangle**: Approximately 20.83 square inches
- **Triangle**: 20.4 square inches

Now we can evaluate each statement:

A. **The triangle area is neither the smallest nor the largest.**
- False, because the triangle (20.4) is larger than the square (20.25) but smaller than the rectangle (20.83).

B. **The rectangle has the largest area.**
- True, as 20.83 > 20.4 and 20.25.

C. **The square area is larger than the rectangle area.**
- False, since 20.25 < 20.83.

D. **The triangle area is smaller than the square area.**
- False, as 20.4 > 20.25.

Thus, the only true statement is:

**B. The rectangle has the largest area.**