Answer:
Area of the trapezoid is 38 cm²
Step-by-step explanation:
- Step 1: Area of the trapezoid can be found by decomposing it into 2 triangles and a rectangle.
- Step 2: Find area of first triangle. Given base = 5 cm and height = 4 cm
Substitute in formula for area of triangle = 1/2 base * height
Area of triangle, A1 = 1/2 * 5 * 4 = 10 cm²
- Step 3: Find area of rectangle. Given breadth = 4 cm (Same as height of triangles) Length = 6 cm. Substitute in formula for area of rectangle = length * breadth
Area of rectangle, A2 = 4 * 6 = 24 cm²
- Step 4: Find area of second triangle. Given height = 4 cm (same as the other triangle) and base = 2 cm (8 cm - 6 cm)
Substitute in formula for area of triangle = 1/2 base * height
Area of triangle, A3 = 1/2 * 2 * 4 = 4 cm²
- Step 5: Calculate total area = A1 + A2 + A3 = 10 + 24 + 4 = 38 cm²
14. 74 fl oz > 8 cups (8 oz=1 c)
15. 12 c = 3 qt (4c=1qt)
16. 18 cup molds (1 c=8 fl oz)
17. 2 pints to make 32 fl oz( 1pt = 16fl oz)
If Ms. Callahan has 24 feet of fencing, and she is building a pen, the PERIMETER of the pen must be 24 feet. The perimeter is basically the distance around a figure. The perimeter of a rectangle is equal to length plus width plus length plus width, AKA l+w+l+w, or P=2l+2w. In a rectangle, two pairs of sides are of equal length--so the two lengths and the two widths must be equal.
So, the formula is P=2l+2w. P, the perimeter, is 24, so 24=2l+2w. Let's try some values for l and see what we get for w. If the length is 1, l=1. 24=(2*1)+2w. 24=2+2w. 22=2w. w=11. So if length is 1 foot, width is 11 feet.
What if l=2? 24=(2*2)+2w. 24=4+2w. 2w=20. w=10. If l=2, w=10. And l=3? 24=(2*3)+2w. 24=6+2w. 18=2w. w=9. If l=3, w=9. Do you see a pattern? Every time we add 1 to l, we subtract 1 from w. So if l=4, w=8. If l=5, w=7. If l=6, w=6. Here, we start getting similar answers: if l=7, w=5. If l=8, w=4. Since we already know these values work, it doesn't matter whether we call it length or width. So, our answers are below.
Answer: Ms Callahan can make a pen with a length of 1 foot and a width of 11 feet, a length of 2 feet and a width of 10 feet, a length of 3 feet and a width of 9 feet, a length of 4 feet and a width of 8 feet, a length of 5 feet and a width of 7 feet, or a length of 6 feet and a width of 6 feet.
Max mows a yard in 45 minutes and Jan takes twice as long mowing the same yard. If Max and Jan both work together, it will take approximately 30 minutes to for them both to mow the yard.
It take Max 1 minute to mow 1/45 of the yard.
It takes Jan 1 minute to mow 1/90 of the yard.
1/45+1/90 =3/90 = 1/30 of the yard can be mowed by both in just one minute. This is how to get the answer, 30 minutes.
