Question

the area of a rectangle in 24 square units. a diagonal drawn from one corner to another divides the rectangle into two right triangles. what is the area of the shaded triangle? 2 x 24 square units 1 x 24 square units \\(\frac{1}{2}\\) x 24 square units \\(\frac{1}{4}\\) x 24 square units

Explanation:

Step1: Recall the property of a rectangle and its diagonal

A diagonal of a rectangle divides the rectangle into two congruent right - triangles. Congruent triangles have equal areas.

Step2: Calculate the area of one of the triangles

Let the area of the rectangle be \(A = 24\) square units. If the area of the rectangle is divided into two equal parts by the diagonal, and let the area of each triangle be \(A_{t}\). Then \(A = A_{t}+A_{t}\) (since the two triangles are congruent). So \(A_{t}=\frac{1}{2}A\).

Answer:

\(\frac{1}{2}\times24\) square units.