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Frank said that you only really need to memorize the area formula for triangles which is because all the other shapes we learned in this week’s lessons can be broken into triangles and you can just find the area of each triangle in the shape and add them together. Is he correct?
Frank is incorrect. Rhombi cannot be broken into triangles.
Frank is incorrect. Trapezoids cannot be broken into triangles.
Frank is correct.
Frank is incorrect. Kites cannot be broken into triangles.
QUESTION 2
I point

Cina said you can usefithe formula for every shape except the triangle. and are the lengths of the diagonals] Is she correct?
She is correct.
She is not correct. The triangle can use this formula too.
She is not correct. The kite cannot use this formula elther.
She is not correct. The trapezoid cannot use this formula elther.

Ask by Hills Simpson. in the United States

Jan 24,2025

Question

My Scores
To-Do List

Frank said that you only really need to memorize the area formula for triangles which is because all the other shapes we learned in this week’s lessons can be broken into triangles and you can just find the area of each triangle in the shape and add them together. Is he correct?
Frank is incorrect. Rhombi cannot be broken into triangles.
Frank is incorrect. Trapezoids cannot be broken into triangles.
Frank is correct.
Frank is incorrect. Kites cannot be broken into triangles.
QUESTION 2
I point

Cina said you can usefithe formula for every shape except the triangle. and are the lengths of the diagonals] Is she correct?
She is correct.
She is not correct. The triangle can use this formula too.
She is not correct. The kite cannot use this formula elther.
She is not correct. The trapezoid cannot use this formula elther.

Ask by Hills Simpson. in the United States

Jan 24,2025

UpStudy AI · Accepted Answer

Let's address each question one by one.

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**QUESTION 1**

**Statement:**
Frank said that you only really need to memorize the area formula for triangles, which is $$ \mathrm{A} = \frac{1}{2} 	imes \mathrm{B} 	imes \mathrm{H} $$, because all the other shapes learned in this week's lessons can be broken into triangles. You can find the area of each triangle in the shape and add them together. Is he correct?

**Options:**
1. Frank is incorrect. Rhombi cannot be broken into triangles.
2. Frank is incorrect. Trapezoids cannot be broken into triangles.
3. Frank is correct.
4. Frank is incorrect. Kites cannot be broken into triangles.

**Answer:**
**Frank is correct.**

**Explanation:**
Most polygonal shapes, including rhombi, trapezoids, and kites, can indeed be divided into triangles. For example:
- **Rhombus:** Can be divided into two congruent triangles by drawing one of its diagonals.
- **Trapezoid:** Can be divided into two triangles by drawing a diagonal.
- **Kite:** Can be divided into two triangles by drawing either of its diagonals.

By calculating the area of each triangle and summing them up, you can find the total area of these shapes. Therefore, memorizing the triangle area formula is sufficient for these cases.

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**QUESTION 2**

**Statement:**
Cina said you can use the formula $$ \mathrm{Area} = k 	imes (D_1 	imes D_2) $$ for every shape except the triangle. $$ D_1 $$ and $$ D_2 $$ are the lengths of the diagonals. Is she correct?

**Options:**
1. She is correct.
2. She is not correct. The triangle can use this formula too.
3. She is not correct. The kite cannot use this formula either.
4. She is not correct. The trapezoid cannot use this formula either.

**Answer:**
**She is not correct. The trapezoid cannot use this formula either.**

**Explanation:**
The formula $$ \mathrm{Area} = \frac{1}{2} 	imes D_1 	imes D_2 $$ is specifically applicable to shapes that have two diagonals that intersect each other at right angles and bisect each other, such as kites and rhombuses. However, not all quadrilaterals can use this formula:
- **Trapezoids:** Generally, trapezoids do not have diagonals that intersect in a way that allows this formula to be used for calculating the area.
- **Rectangles and Squares:** While they have diagonals, their area is more straightforwardly calculated using length and width.

Moreover, triangles do not have diagonals, so the formula does not apply to them either. Therefore, Cina's statement is incorrect because there are shapes other than triangles (like trapezoids) for which the formula is not applicable.

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**Summary of Correct Answers:**
1. **Frank is correct.**
2. **She is not correct. The trapezoid cannot use this formula either.**
Frank is correct. Cina is not correct.

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