Answer:
The area of the trapezoid is 57.5 in.²
Step-by-step explanation:
The given information of the trapezoid are;
The vertices of the trapezoid = QRST
The altitude of the trapezoid = 5 in.
The shape the altitude divides the trapezoid into = A square and an isosceles right triangle
The long side of the rectangle = 9 in.
Therefore, we have;
The legs of an isosceles right triangle are equal
Given that one of the legs of the isosceles right triangle = The altitude of the triangle = 5 in.
Therefore, for the isosceles triangle, the length of the other leg = 5 in.
Therefore;
The area of the right triangle = 1/2 × Base × Height (altitude)
The area of the right triangle = 1/2 × Leg × leg = 1/2 × (Leg)²
∴ The area of the right triangle = 1/2 × 5 in. × 5 in. = 12.5 in.²
The length of the rectangle is given as l = 9 in.
The height of the rectangle, h = The altitude of the rectangle = 5 in.
The area of the rectangle, A = l × h
∴ The area of the rectangle, A = 9 in. × 5 in. = 45 in.²
The area of the trapezoid = The area of the right triangle + The area of the rectangle
The area of the trapezoid = 12.5 in.² + 45 in.² = 57.5 in.²
