Question

select the correct answer from each drop-down menu.

a designer makes the sketch shown below for a new lamp. what is the approximate area of her sketch?

the lamp shade is a trapezoid. its area is approximately choose an answer square inches. the bases of the lamp are two trapezoids. the area of each is approximately choose an answer square inches. in total, the area is approximately choose an answer square inches.

Explanation:

⚡ Using what you learned: Area of Trapezoids and Other Polygons

Step 1: Area of the lamp shade

The lamp shade is a trapezoid. Looking at the diagram:

• The top base is \( b_1 = 4\text{ in} \).
• The bottom base is equal to the width of the middle section, which is \( b_2 = 6\text{ in} \).
• The height is \( h = 6\text{ in} \).

Using the trapezoid area formula:

$$ A = \frac{1}{2} \cdot (b_1 + b_2) \cdot h $$

$$ A = \frac{1}{2} \cdot (4 + 6) \cdot 6 = \frac{1}{2} \cdot 10 \cdot 6 = 30\text{ sq in} $$

Step 2: Area of each base trapezoid

The base of the lamp consists of two identical trapezoids joined together. Looking at the bottom section:

• The total height of this section is \( 8\text{ in} \), so each of the two trapezoids has a height of \( h = 4\text{ in} \).
• The middle shared base is \( b_1 = 6\text{ in} \).
• The top and bottom outer bases are \( b_2 = 4\text{ in} \) (matching the width of the lamp shade's top base).

Using the trapezoid area formula for one of these base trapezoids:

$$ A = \frac{1}{2} \cdot (6 + 4) \cdot 4 = \frac{1}{2} \cdot 10 \cdot 4 = 20\text{ sq in} $$

Step 3: Total area of the sketch

Sum the area of the lamp shade and the two base trapezoids:

$$ \text{Total Area} = 30 + 20 + 20 = 70\text{ sq in} $$

Answer:

• The lamp shade is a trapezoid. Its area is approximately 30 square inches.
• The bases of the lamp are two trapezoids. The area of each is approximately 20 square inches.
• In total, the area is approximately 70 square inches.