Question

4
5.
6.
find the missing measurement for each triangle. show your steps!
7.
b = 20 m
h = ?
a = 150 m²
8.
b = ?
h = 10 cm
a = 225 cm²
9.
b = 18 m
h = ?
a = 162 m²

1. a triangular - shaped sign has a base of 15 ft, and a height of $8\frac{2}{5}$ ft. what is the area of the sign?

Explanation:

Step1: Recall triangle area formula

The area of a triangle is $A = \frac{1}{2}bh$, where $b$ = base, $h$ = height.

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For Problem 7:

Step1: Rearrange for height $h$

$h = \frac{2A}{b}$

Step2: Substitute given values

$h = \frac{2 \times 150}{20}$

Step3: Calculate the result

$h = 15$

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For Problem 8:

Step1: Rearrange for base $b$

$b = \frac{2A}{h}$

Step2: Substitute given values

$b = \frac{2 \times 225}{10}$

Step3: Calculate the result

$b = 45$

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For Problem 9:

Step1: Rearrange for height $h$

$h = \frac{2A}{b}$

Step2: Substitute given values

$h = \frac{2 \times 162}{18}$

Step3: Calculate the result

$h = 18$

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For Problem 10:

Step1: Convert mixed number to fraction

$8\frac{2}{5} = \frac{42}{5}$

Step2: Apply area formula

$A = \frac{1}{2} \times 15 \times \frac{42}{5}$

Step3: Simplify and calculate

$A = \frac{1}{2} \times 126 = 63$

Answer:

1. $h = 15$ m
2. $b = 45$ cm
3. $h = 18$ m
4. $63$ ft²