Area of Shapes with four sides

Find the area of the parallelogram. Height is 9 and base is 12.

108 The formula for the area of a parallelogram is simply the base times the height: A=bh. Notice that this is the essentially the same as the formula for the area of a rectangle which is length times width: A=lw. This is because if you take the triangle from one end of a parallelogram and move it to the other end, you will have a rectangle, so the area is the same. In this case we have a base of 12 and a height of 9 so A=12×9=108. The area of the parallelogram is 108 square units

The area of a rectangle is 216 square meters. The length is 18 meters. What is the width? Give your answer without units.

12 To find the area of a rectangle, multiply the length times the width. In this problem, because the width is not known, use the formula and work backward. Write the formula: A=l⋅w Fill in the known values: 216=18⋅w Divide both sides by 18: A=12 The width of the picture frame is 12 meters.

What is the area of the parallelogram in the figure below? Write your answer in fraction form. base 9, height 7.5

135/2 The formula for the area of a parallelogram is A=l⋅h where l is the length of the parallelogram and h is the height of the parallelogram. In this case, h=7.5=152 and l=9. Thus, A=152⋅9=135/2.

Find the area of the parallelogram in the figure below. Round your final answer to the nearest tenth.

15.4 The formula for the area of a parallelogram is A=lh where l is the length of the parallelogram and h is the height of the parallelogram. In this case, h=2.3 and l=6.7. Thus, A=(6.7)(2.3)=15.41. Rounding the answer to the nearest tenth gives us A=15.4.

Area for parallelogram with No given height. C 11.4, A 4, , length 15

160.1 Step 1 : Using the Pythagorean Theorem, we can determine that the height of the parallelogram is 10.675 units in length. We can then calculate the area to be (10.675)(15)=160.1 units squared, rounded. Step 2: The formula for the area of a parallelogram is A=lh where l is the length of the parallelogram and h is the height of the parallelogram. In this case, we are not given the height, but can calculate it using the Pythagorean theorem, h2+a2=c2 or h2=c2−a2. Using the values for c and a from the given parallelogram, h2=11.42−42=113.96, Take the square root of both sides of the equation. h2−−√=113.96−−−−−√ hence h=10.675. We can now plug our values for h and l into the formula for area. Thus, A=(10.675)(15)=160.125. Rounding to the nearest tenth, A=160.1.

Find the area of the trapezoid in the figure below. Round your final answer to the nearest tenth. Hypotenuse 7.2, 5, and height 4, base 2. Missing base.

26 First we must calculate the length of the second base of the trapezoid. We are given the hypotenuse of the triangles created from the sides and height of the trapezoid, therefore, we can calculate the length of the missing base using the Pythagorean theorem. Calculate the base, a of the triangle with a hypotenuse of 5, a2=52−42=9. Taking the square root of both sides, a=3. Calculating the base b of the triangle with a hypotenuse of 7.2, b2=7.22−42=35.84. Again, square rooting both sides of the equation leaves b=5.99. Hence the top base of the trapezoid is 3+2+5.99=10.99. Thus the area of the trapezoid is, A=4(2+10.99)/2=25.98. Rounding this to the nearest tenth, A=26.0.

The length of a rectangle is 81 meters and the width is 47 meters. Find the area. Give your answer without units.

3807 To find the area of a rectangle, we multiply the length times the width. When we multiply these numbers we find 81×473807 So the area of the rectangle is 3807 meters squared.

The length of a rectangle is 90 meters and the width is 85 meters. Find the area. Give your answer without units.

7650 Write the formula to find the area of a rectangle: A=l⋅w Fill in known values: A=90⋅85 Multiply: A=7650 The area of the rectangle is 7650 square meters.

Find the area of the trapezoid in the figure below. Base 9, base 15, height 7

84 We are given the bases b1 and b2 along with the height of the trapezoid in the problem statement. Therefore, the area of the trapezoid is, A=7(9+15)/2=84.

The length of a rectangle is 99 meters and the width is 87 meters. Find the area. Give your answer without units.

8613 To find the area of a rectangle, we multiply the length times the width. When we multiply these numbers we find 99×878613 So the area of the rectangle is 8613 meters squared.

Area of a trapezoid with height 8, base 9, base 14.

92 The formula for the area of a trapezoid is the sum of the two bases times the height, times 12 (or divided by 2): A=12⋅h⋅(b1+b2). This formula works because if you put this trapezoid together with an upside-down copy of itself, it would form a parallelogram with the same height, h and a base the size of both bases of the trapezoid combined, (b1+b2). The area of the trapezoid would be half the area of this parallelogram, or A=12⋅h⋅(b1+b2). In this case our two bases have lengths 14 and 9 and our height is 8. Plugging these into our formula, we get: A=12(8)(14+9)=12(8)(23)=12(184)=92

Find the area of the trapezoid. Height 8, base 14, base 9.

92 The formula for the area of a trapezoid is the sum of the two bases times the height, times 12 (or divided by 2): A=12⋅h⋅(b1+b2). This formula works because if you put this trapezoid together with an upside-down copy of itself, it would form a parallelogram with the same height, h and a base the size of both bases of the trapezoid combined, (b1+b2). The area of the trapezoid would be half the area of this parallelogram, or A=12⋅h⋅(b1+b2). In this case our two bases have lengths 14 and 9 and our height is 8. Plugging these into our formula, we get: A=12(8)(14+9)=12(8)(23)=12(184)=92

Find the area of the trapezoid missing base. Round your final answer to the nearest tenth. Length 30.5, base 13.5, height 26.

Step 1: Using the Pythagorean Theorem, we can determine that the second base of the trapezoid is 45.4 units in length. We can then calculate the area to be 26(45.4+13.5)/2=765.7 units squared First we must calculate the length of the second base of the trapezoid. We are given the hypotenuse of the triangles created from the sides and height of the trapezoid, therefore, we can calculate the length of the missing base using the Pythagorean theorem, 30.52=262+b2. This means that b2=930.25−676=254.25. Taking the square root of both sides, b=15.95. Because the two triangles that are formed with the sides and height of the trapezoid are the same measurements, we can conclude that the length of the missing base will be 15.95+15.95+13.5=45.4. Thus the area of the trapezoid will be, A=26(45.4+13.5)/2=765.7.