Question

use the triangle area formula ( a = \frac{1}{2}bh ) to fill in the chart below.
label the base and height in the triangles to the right.

1. pamela wants to plant a triangular garden in her backyard and has space. she wants the base of her garden to line up against the back of her shed which is length. what will be the height of her garden?
2. if pamela increases the area of her garden but keeps the length of the base (she wants the base of the garden to line up against the shed) what will she have to do to the height of the garden?
3. howard is laying triangular tiles in his bathroom. the area of each tile is 6 square inches and the height is 4 inches. what is the length of the base of each tile?
4. if howard swaps out his tiles for ones that have a height bigger than 4 inches but wants to keep the area the same what will he have to do to the base of each tile?
5. sam geometer is drawing a model for his father’s tree farm. his model trees must all fit on a piece of paper that is 3 ft. x 3 ft. he started making a chart to help him keep track of all the trees, but forgot to fill in everything as he went. he needs to finish the chart to show his father, but only has a short time to do it. he uses the area formula for a triangle and manipulates it so he can solve for each column by just putting the numbers in the calculator to find the missing piece of information.

a) what are the equations sam used for each column? \tarea column ( a = \frac{1}{2}bh ) \tbase column ( b = ) \theight column ( h = )
b) finish filling in sam’s chart.

( a = \text{area} )	( b = \text{base} )	( h = \text{height} )
	2 cm	8 cm
	8 cm	19 cm
25 cm²	10 cm
10 cm²	2 cm
42 cm²	6 cm
20 cm²		8 cm
90 cm²		12 cm

Explanation:

Answer:

a) Base Column: \( b = \frac{2A}{h} \), Height Column: \( h = \frac{2A}{b} \)
b)

\( A \) (cm²)	\( b \) (cm)	\( h \) (cm)
8	2	8
76	8	19
25	10	5
10	2	10
42	6	14
20	5	8
90	15	12

(Note: For each row, use \( A = \frac{1}{2}bh \), \( b = \frac{2A}{h} \), or \( h = \frac{2A}{b} \) to calculate the missing value. Example calculations:

• First row: \( A = \frac{1}{2}(10)(5) = 25 \)
• Fourth row: \( h = \frac{2(25)}{10} = 5 \)
• Fifth row: \( h = \frac{2(10)}{2} = 10 \)
• Sixth row: \( h = \frac{2(42)}{6} = 14 \)
• Seventh row: \( b = \frac{2(20)}{8} = 5 \)
• Eighth row: \( b = \frac{2(90)}{12} = 15 \))