Question

which statement is true of the right triangles abc and def? area of abc is greater than area of def. area of abc is less than area of def. area of abc is equal to the area of def. there is not enough information to compare the areas of triangles abc and def.

Explanation:

Step1: Identify base/height of DEF

From the grid: Right triangle DEF has base $|DF_x - F_x| = |0 - 6| = 6$, height $|D_y - F_y| = |8 - 0| = 8$.
Area formula: $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$
$\text{Area of DEF} = \frac{1}{2} \times 6 \times 8 = 24$

Step2: Identify base/height of ABC

From the grid: Right triangle ABC has base $|C_x - A_x| = |6 - (-8)| = 12$, height $|B_y - A_y| = |-4 - (-10)| = 6$.
$\text{Area of ABC} = \frac{1}{2} \times 12 \times 6 = 36$

Step3: Compare the two areas

$36 > 24$, so area of ABC > area of DEF.

Answer:

Area of ABC is greater than area of DEF.