need help showing my work with question below.

Question

triangle PQR and triangle QRS have vertices P(-9,7) Q(4,7), R(4,-3), and S(10-3). what is the area in sq. units, of quadrilateral PQSR which is formed by the two triangles?

 

Answer Is 95. How To Get That Answer Showing Work

Answer 1

The easiest way to solve the problem is to plot all the given points in the coordinate plane. You will notice that the figure formed is a trapezoid whose bases have lengths 6 and units, respectively, and whose height is 10 units.

By applying the formula for Area of a trapezoid: A = (1/2)(b₁ + b2)(h) and substituting  the obtained values such as; h = 10, b₁= 6, b₂ = 13, hence

A = 1/2(6 + 13)(10).

So A = 95 Square units.

Therefore, the area of the quadrilateral formed is 95 square units.

Make sense? There are many ways to find the correct answer to such type of question, but sometimes teachers requires you to use methods which they think appropriate to the existing or current lesson.

Answer 2

Since the quadrilaterl is formed by two triangles PQR and QRS, the area of the quadrilateral is equal to the sum of the areas of the two triangle. So, you have to find the areas of the triangle and add them up to get the answer. Following is how you do the calculations.

For triangle PQR, find the length of each sides: PQ, QR and RP using the formula of length between two points: length between 2 points (x1,y1) and (x2,y2) is Sq.root of {(x1-x2)^2+(y1-y2)^2}

Once you have 3 sides PQ, QR and RP, find the area of the triangle, 

Area of PQR = sq.root of (s(s-PQ)(s-QR)(s-RP)) where s = (PQ+QR+RP)/2 also known as semi-perimeter.

Similarly, find the area of triangle QRS using the same technique.

After doing that, you can just add the two areas to get the area of quadrilateral PQRS:

Area of Quadrilateral = Area of triangle PQR + Area of triangle QRS