Question 34·Easy·Area and Volume
In the figure, rectangle is divided by diagonal .
Which choice is the area of triangle , in square units?
When a rectangle is cut by a diagonal, the two triangles formed are congruent and have equal area. So you can quickly compute the rectangle’s area using base times height, then divide by 2 to get the area of either triangle.
Hints
Use the labeled side lengths
Read the lengths of two adjacent sides of the rectangle from the figure.
Connect diagonal to area
A diagonal of a rectangle creates two triangles with equal area.
Half of what?
Find the rectangle’s area, then take half of it.
Desmos Guide
Enter the side lengths
Type a=8 and b=6 to represent the rectangle’s side lengths from the figure.
Compute the rectangle’s area
Type A=a*b and note the value of .
Take half for the triangle
Type T=A/2 and use the value of as the area of triangle .
Step-by-step Explanation
Find the area of the rectangle
From the figure, and , so the rectangle’s area is square units.
Take half for triangle
Diagonal divides rectangle into 2 congruent triangles, so each triangle has half the rectangle’s area: . Therefore, the area of triangle is square units.