Question

mixed review

1. find the area of the shaded triangle. show your reasoning.
2. andre drew a line connecting two opposite corners of a parallelogram. select all true statements about the triangles created by the line that andre drew.

a. each triangle has two sides that are 3 units long.
b. each triangle has a side that is the same length as the diagonal line.
c. each triangle has one side that is 3 units long.
d. when one triangle is placed on top of the other and their sides are aligned, we will see that one triangle is larger than the other.
e. the two triangles have the same area as each other.

Explanation:

1.

Step1: Find the base and height of the shaded triangle

The base of the shaded triangle is 6 units and the height is 6 units.

Step2: Use the triangle - area formula

The area formula for a triangle is $A=\frac{1}{2}bh$. Substitute $b = 6$ and $h = 6$ into the formula: $A=\frac{1}{2}\times6\times6$.

Step3: Calculate the area

$A=\frac{1}{2}\times36 = 18$ square units.

When a diagonal is drawn in a parallelogram, the two triangles formed are congruent. Congruent triangles have the same shape and size, so they have the same area. Also, the diagonal is a common side for the two triangles.

Answer:

18 square units

2.