Question

Find the area of the rectangle or triangle.

Short answer

Area of the Triangle is 39 – 13y sq unit.

Step-by-step solution

Step-1 – Apply the concept of Triangle 

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

Step-2 – How to find the area of Triangle? 

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

Step-3 – Distributive Property of Multiplication 

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

Distributive Property of Multiplication

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

Example: $\text{12} \text{(6} \text{-} \text{4} \text{)} = \text{12} · \text{6} - \text{12} · \text{4} = 72 - 48 = 24$

Find the area of the Rectangle.

In this figure the base is 6 – 2y and height = 13

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

Find the area, using the distributive method of multiplication.

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

Area =$\frac{1}{2} · \text{( 6}-\text{2y)} · \text{13} = (3 - y) · 13\text{= 3} · \text{13} - y · 13 = 39 - 13y$square units

Area of the Triangle is 39 – 13y sq unit.