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VMariaS [17]
2 years ago
15

What is the total area of the figure? (square inches)

Mathematics
2 answers:
Radda [10]2 years ago
7 0

Answer:

60

Step-by-step explanation:

TOTAL SURFACE AREA = AREA OF SQUARE+2×(AREA OF TRIANGLE)

=(6×6)+2×(1/2×6×4)

=36+24=60 square inches

I hope it helped you

marshall27 [118]2 years ago
4 0

Answer:

The area of the full figure is 60 square inches.

Step-by-step explanation:

There are 4 triangles and one square in this figure. We can start by figuring out the area of the middle square, which would be 6*6=36 because we know the sides are all 6 inches.

Next, we can look at the triangles and see that their hypotenuses (the longest sides) are all the same length, that being 5 inches. This means that we only need to find the length of the third side and then multiply the area of one triangle by 4 to get the area of all the triangles.

The pythagorean theorem states that in any right triangle, a^2 +b^2=c^2, with c^2 being the length of the hypotenuse. Since we know the length of the hypotenuse is 5 and one of the legs of the triangle is 4, we can insert this into the equation: a^2+4^2=5^2, which when simplified all the way gives us that a=3.

Since a right triangle is half of a rectangle, the easiest way to find the area of the triangle is to multiply the measures of the two legs together and then divide by two: (3*4)/2=6. Therefore, we know that each triangle in the picture has an area of 6.

Finally, you need to add all of the areas together to find the area of the full figure: 36+6+6+6+6=60 in^2

The area of the full figure is 60 square inches.

Hope this helps! :)

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Length of the base of the given triangle is (x+3) units and the perpendicular height is (x-1)units. If the area of the triangle
Lana71 [14]

Step-by-step explanation:

the area of a triangle is

baseline × height / 2

so, in our case we know this is 10 :

(x+3)(x-1)/2 = 10

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the general solution to a quadratic equation is

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= -1 + 2×2.45 = -1 + 4.9 = 3.9 ≈ 4

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or using sqrt(6) ≈ 2.45

= -1 - 2×2.45 = -1 - 4.9 = -5.9 ≈ -6

x2 would give us negative lengths for the triangle, which does not make sense.

so, x = 4 is our solution.

and that makes the height x-1 = 4-1 = 3 units.

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