QUESTION 1. Find the area. (Round to the nearest hundredth) QUESTION 2. Trapezoid QRST has two right angles. A 5in altitude can be drawn dividing QRST into a rectangle and an isosceles right triangle. The longer side of the rectangle measures 9in. What is the area of the trapezoid ?

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

7. d. 64

8. i. 32

9. c. 125

10. j. none of the above

11. d. 81

12. i. 216

13. e. none of the above

14. g. 240

15. e. none of the above

16. g. 32

17.   e. none of the above