Question

You are building a shelf that fits in a corner. In the figure, the entire shelf is △XYZ. Each unit in the coordinate plane represents one inch. Find area A on the shelf.

Answer 1

Given:

The vertices of the traingle XYZ are X(15,20), Y(15,5), and Z(0.5).

Required:

We need to find the area of the triangle XYZ.

Explanation:

The given traingle XYZ is a right-angled triangle.

The height of the triangle is XY.

The side of the base is ZY.

Consider the distance formula.

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

The distance between the points (15,20) and (15,5) is

$Substitute\text{ }x_2=15,x_1=15,y_2=5,\text{ and }y_1=20\text{ in the formula.}$

$d=\sqrt{(15-15)^2+(5-20)^2}$$d=\sqrt{0+(-15)^2}=\sqrt{15^2}$$d=15$

We get h =15 since the distance between (15,20) and (15,5) is height.

The distance between the points (0,5) and (15,5) is

$Substitute\text{ }x_2=15,x_1=0,y_2=5,\text{ and }y_1=5\text{ in the distance formula.}$$d=\sqrt{(15-0)^2+(5-5)^2}$$d=\sqrt{(15)^2+(0)^2}=\sqrt{15^2}$$d=15$

We get b=15 since the distance between (0.5) and (15,5) is the base.

Consider the area of the triangle formula.

$A=\frac{hb}{2}$

Substitute h =15 and b =15 in the formula.

$A=\frac{15\times15}{2}$$A=112.5untis^2$

Given that each unit in the coordinate plane represents one inch.



$A=112.5inches^2$

Final answer:

$A=112.5in^2$