The area of a triangle calls for a base and a perpendicular height. In a rectangle split by a diagonal, two sides that meet at a corner give those lengths. The diagonal makes two equal-area triangles, so type half the product into Desmos. Multiplying the sides without halving finds the whole rectangle, not the requested triangle.
Hints
- Hint 1
A triangle's base can be one of its sides. Its height must meet that base at a right angle. Which two labeled sides meet at the rectangle's corner ?
- Hint 2
A diagonal of a rectangle makes two triangles with equal area, the space each covers. Each triangle takes half the rectangle. How should you adjust the product of the two side lengths?
Step-by-step
Use half the rectangle
Step 1Identify the base and height
At , sides and meet at a right angle because is a rectangle. For triangle , use as the base and as the perpendicular height. The slanted diagonal isn't the height.
- Step 2
Write the triangle's area
The diagonal cuts the rectangle into two triangles with equal area. Each triangle has half the rectangle's area. So use half the base-height product:
- Step 3
Calculate the area
Type into Desmos. It shows , so the area of triangle is square units. Choice B.