---**Darren made a display board in the shape of a trapezoid.**### Part A**The height of the trapezoid is half the length of the shorter base, and the longer base is twice the length of the shorter base.**![Trapezoid](trapezoid.png)[Diagram of a trapezoid]- The shorter base has a length given as $2 \text{ yd}$.- The height of the trapezoid $h$ is marked with a dashed line.- The longer base $b$ is labeled at the bottom.The given dimensions are:- Shorter base (top) = $4 \text{ yd}$- Left side segment = $2 \text{ yd}$- Right side segment = $2 \text{ yd}$**What are the lengths of the height and the longer base? Enter your answers in the boxes.**- $h = \_\_\_\_ \text{ yd}$- $b = \_\_\_\_ \text{ yd}$### Part B**Use the measurements from Part A to find the area of Darren's display board.**- [ ] $8 \text{ yd}^2$- [ ] $12 \text{ yd}^2$- [ ] $16 \text{ yd}^2$- [ ] $24 \text{ yd}^2$---This problem involves using the properties of trapezoids to determine the height and the bases, followed by calculating the area of a trapezoid. A trapezoid is a quadrilateral with at least one pair of parallel sides, called bases. The height is the perpendicular distance between these bases. To find the area of the trapezoid, you use the formula:\[ \text{Area} = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height} \]In this problem, you will calculate the height and the longer base using the given relationships and then use these values to find the area of the trapezoid display board.

The area of a trapezoid is one-half of the product of the sum of the lengths of the parallel sides…

Part A The height of the trapezoid is half the length of the shorter base, and the longer base is twice the length of the shorter base. 4 yd 2 yd 2 yd b. What are the lengths of the height and the longer base? Enter your answers in the boxes. h = yd

Part A The height of the trapezoid is half the length of the shorter base, and the longer base is twice the length of the shorter base. 4 yd 2 yd 2 yd b. What are the lengths of the height and the longer base? Enter your answers in the boxes. h = yd

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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A: Trapezoid

Question

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---

**Darren made a display board in the shape of a trapezoid.**

### Part A
**The height of the trapezoid is half the length of the shorter base, and the longer base is twice the length of the shorter base.**

![Trapezoid](trapezoid.png)

[Diagram of a trapezoid]

- The shorter base has a length given as $2 \text{ yd}$.
- The height of the trapezoid $h$ is marked with a dashed line.
- The longer base $b$ is labeled at the bottom.

The given dimensions are:
- Shorter base (top) = $4 \text{ yd}$
- Left side segment = $2 \text{ yd}$
- Right side segment = $2 \text{ yd}$

**What are the lengths of the height and the longer base? Enter your answers in the boxes.**

- $h = \_\_\_\_ \text{ yd}$
- $b = \_\_\_\_ \text{ yd}$

### Part B
**Use the measurements from Part A to find the area of Darren's display board.**

- [ ] $8 \text{ yd}^2$
- [ ] $12 \text{ yd}^2$
- [ ] $16 \text{ yd}^2$
- [ ] $24 \text{ yd}^2$

---

This problem involves using the properties of trapezoids to determine the height and the bases, followed by calculating the area of a trapezoid. A trapezoid is a quadrilateral with at least one pair of parallel sides, called bases. The height is the perpendicular distance between these bases. To find the area of the trapezoid, you use the formula:

\[ \text{Area} = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height} \]

In this problem, you will calculate the height and the longer base using the given relationships and then use these values to find the area of the trapezoid display board.

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