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Helen [10]
3 years ago
14

Find the area of the trapezoid. leave your answer in simplest radical form.

Mathematics
2 answers:
uranmaximum [27]3 years ago
5 0

Answer:

Area = 170 ft^2

Step-by-step explanation:

Area of Trapezoid is given by the formula  A=\frac{1}{2}(b_1+b_2)h

Where

b1 and b2 are the two bases (parallel sides)

h is the height

<em>In our diagram, the two bases are 12 and 22, but the height (let it be h) isn't given.</em> To find the height (the dotted line), we use the right triangle which has an angle given as 45°.

Since the height is the "opposite" side to angle and we know the base of the triangle (22-12=10), which is the "adjacent" side, we can use the ratio of tan. Note, tan 45° = 1.

Tan(45)=\frac{h}{10}\\h=Tan(45)*10\\h=1*10\\h=10

Now we can plug the information into the formula and solve for area. So:

Area = A=\frac{1}{2}(b_1+b_2)h\\A=\frac{1}{2}(12+22)(10)\\A=\frac{1}{2}(34)(10)\\A=170

Thus Area = 170 ft^2

Alik [6]3 years ago
4 0

Answer:

170 ft²

Step-by-step explanation:

We can divide this figure into two parts.

We have the rectangle part and the triangle,

Area of the triangle = 1/2 bh

base = 22 - 12 = 10 ft

height = 10×tan 45°

            = 10 × 1 = 10 ft

∴ Area = 1/2 × 10 × 10

            = 50 ft²

Area of the rectangle = length × width

length = 12 ft

width = 10 ft

Area = 12 × 10

        = 120 ft²

Total area of the trapezoid = 120 + 50

                                            = 170 ft²

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In total 10 solutions for x_1=1.

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4. Add all numbers of solutions:

11+10+9+8+7+6+5+4+3+2+1=66.

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