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A triangle is a closed figure bounded by three line segments.

The area of a closed plane figure is the measure of the region (surface) by its boundary.

Area of Triangle = $\frac{1}{2}  ·  \text{base}  ·  \text{height}$square unit

Suppose a, b, and c is three real numbers.

Distributive Property of Multiplication

Property: $\text{a}  \text{(b}  \text{+}  \text{c}  \text{)}  =  \text{a}  ·  \text{b}  +  \text{a}  ·  \text{c}  $

Example: $\text{12}  \text{(3}  \text{+}  \text{4}  \text{)}  =  \text{12}  ·  \text{3}  +  \text{12}  ·  \text{4}  =  36  +  48  =  84$

In this figure the base is 18 and height = 5a + 7

We know that area of Triangle =$\frac{1}{2}  ·  \text{base}  ·  \text{height}$

Find the area, using the distributive method of multiplication.

Property: $\text{a}  \text{(b}  \text{+}  \text{c}  \text{)}  =  \text{a}  ·  \text{b}  +  \text{a}  ·  \text{c}  $

Area =$\frac{1}{2}  ·  \text{18}  ·  \text{(5a+7)}  =  9  ·  \text{(5a+7) = 9}  ·  \text{5a}  \text{+}  9  ·  7  =  45a  +  63$square units

Area of the Triangle is 45a + 63 sq unit.