Question

spaced review
practice concepts from previous topics.
1 determine the lcm of each pair of numbers.
a 8 and 12 b 9 and 15
2 determine the area of a triangle that has a height of 4 feet and a base of 6\frac{1}{2} feet.
3 write a fact family relating each set of numbers.
a \frac{3}{4}, \frac{1}{2}, \frac{3}{8} b \frac{1}{3}, 6, 2
4 calculate the surface area of a cube that has a width of 25 centimeters.
5 determine each quotient.
a \frac{3}{4} \div \frac{1}{8} b \frac{4}{5} \div \frac{1}{3} c 12\frac{3}{4} \div 1\frac{1}{5}
6 calculate the area of each shape.
a triangle with base 36 in, height 20 in b trapezoid with top base 8 ft, bottom base 14 ft, height 5 ft
7 consider the triangular prism with dimensions 30 cm, 12 cm, 15 cm, 17 cm, 17 cm.
a draw a net of the solid and label its dimensions.
b calculate the surface area of the solid.
8 consider the rectangular prism shown with length 2\frac{1}{2} in, width 1\frac{3}{4} in, height 3 in.
a determine the number of \frac{1}{4}-inch cubes that can pack the prism.
b calculate the volume of the rectangular prism.

Explanation:

Let's solve problem 2: Determine the area of a triangle that has a height of 4 feet and a base of \( 6\frac{1}{2} \) feet.

Step 1: Recall the formula for the area of a triangle

The formula for the area \( A \) of a triangle is \( A = \frac{1}{2} \times \text{base} \times \text{height} \).

Step 2: Substitute the given values into the formula

The base \( b = 6\frac{1}{2} \) feet, which is equal to \( \frac{13}{2} \) feet (since \( 6\frac{1}{2} = \frac{6 \times 2 + 1}{2} = \frac{13}{2} \)), and the height \( h = 4 \) feet.

Substituting these values into the formula:
\[
A = \frac{1}{2} \times \frac{13}{2} \times 4
\]

Step 3: Simplify the expression

First, multiply \( \frac{1}{2} \) and 4:
\[
\frac{1}{2} \times 4 = 2
\]

Then, multiply this result by \( \frac{13}{2} \):
\[
2 \times \frac{13}{2} = 13
\]

Answer:

The area of the triangle is 13 square feet.