Question

1. a right triangle is shown below. calculate the area, in square feet, of the triangle.

(image of right triangle with legs 22 ft and 25 ft)

1. an isosceles trapezoid is shown to the right. what is the area, in square centimeters, of the isosceles trapezoid?

(image of isosceles trapezoid with top base 10 cm, bottom base 16 cm, height 15 cm)
homework 4.1 continued

1. a regular hexagon is made of equilateral triangles, as shown below

(image of regular hexagon with side 5 cm, height of triangle 4.3 cm)
what is the area, in square centimeters, of this regular hexagon?
(a) 16.76
(b) 21.5
(c) 34.3
(d) 64.5

1. (review) ben has 1 ¼ pounds of nuts. he wants to create ⅛ pound baggies to share with friends. how many baggies will he make?

Explanation:

First Problem (Right Triangle Area)

Step1: Recall right triangle area formula

The area of a right triangle is given by \( A = \frac{1}{2} \times \text{base} \times \text{height} \).

Step2: Identify base and height

From the diagram, base \( b = 25 \) ft and height \( h = 22 \) ft.

Step3: Substitute into formula

\( A = \frac{1}{2} \times 25 \times 22 \)
\( A = 12.5 \times 22 \)
\( A = 275 \) square feet.

Step1: Recall trapezoid area formula

The area of a trapezoid is \( A = \frac{1}{2} \times (a + b) \times h \), where \( a \) and \( b \) are the lengths of the two parallel sides, and \( h \) is the height.

Step2: Identify values

Here, \( a = 10 \) cm, \( b = 16 \) cm, and \( h = 15 \) cm.

Step3: Substitute into formula

\( A = \frac{1}{2} \times (10 + 16) \times 15 \)
\( A = \frac{1}{2} \times 26 \times 15 \)
\( A = 13 \times 15 \)
\( A = 195 \) square centimeters.

Step1: Recall hexagon as 6 equilateral triangles

A regular hexagon can be divided into 6 equilateral triangles (or in this case, triangles with base 5 cm and height 4.3 cm). The area of one triangle is \( \frac{1}{2} \times \text{base} \times \text{height} \), and the hexagon area is 6 times that.

Step2: Calculate area of one triangle

For one triangle, base \( b = 5 \) cm, height \( h = 4.3 \) cm.
Area of one triangle: \( \frac{1}{2} \times 5 \times 4.3 = 2.5 \times 4.3 = 10.75 \) square cm.

Step3: Calculate hexagon area

Hexagon area: \( 6 \times 10.75 = 64.5 \) square cm.

Answer:

275 square feet

Second Problem (Isosceles Trapezoid Area)