# How do you write a function rule for the area of a triangle with a base 10 cm less than 8 times the height. What is the area of the triangle when its height is 5 cm?

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Nimo N. Share
Jan 7, 2018

$A \left(H\right) = 4 {H}^{2} - 5 H$
$A \left(5 c m\right) = 75 c {m}^{2}$

#### Explanation:

Area of a triangle with a base 10 cm less than 8 times the height.
Area of a triangle: $A = \frac{1}{2} \cdot B \cdot H$

Relationship between B and H:
$B = 8 \cdot H - 10$

It is unspecified whether the area should be in terms of its base or height, A(H) will be used, especially in light of the second part of the question.

So, substitute the expression for B into the area equation.
$A \left(H\right) = \frac{1}{2} \cdot \left(8 H - 10\right) \cdot H$
$A \left(H\right) = \left(4 H - 5\right) \cdot H$
$A \left(H\right) = 4 {H}^{2} - 5 H$

Area of the triangle when its height is 5 cm?
$A \left(5\right) = 4 {\left(5\right)}^{2} - 5 \left(5\right)$
$A \left(5\right) = 100 - 25 = 75$
$A \left(5 c m\right) = 75 c {m}^{2}$

Check:
Given that the base is $10 c m \text{ less than " (8*5cm) ", so it is } 30 c m$
Area calculation:
$\frac{1}{2} \cdot 30 c m \cdot 5 c m = 15 c m \cdot 5 c m = 75 c {m}^{2}$

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