The length of the hypotenuse of the triangle is 10 units and the area of the composite figure is 34 square units
From the help of Pythagoras' Theorem, since we are given the information that the triangle r is a right-angled triangle with a right angle at the vertex, The lengths of sides AB and BC are 5√2 units and So from the formula, we find the hypotenuse which AC, we write :
AC²=AB²+BC²
=>h²= (5√2)² +(5√2)²
=>h =√( 2(5√2)²) = 10 units
The figure can be referred to as a trapezoid with a rectangle removed. So the area of the trapezoid is :
A = (1/2)(b1 +b2)h
A = (1/2)(10 +6)(5) = 40
Since The area of the rectangle is:
A = LW
A = (3)(2) = 6
then the shaded portion area will be :
shaded area = trapezoid area - rectangle area
= 40 - 6 = 34 .
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