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2 years ago

Use the right triangular prism to find the total surface area of the prism. Leave label off answer.

Mathematics

1 answer:

9966 [12]2 years ago

4 0

Step-by-step explanation:

the total surface area is the sum of the 5 individual areas in the surface :

2 triangle sides (left and right).

1 back rectangle side

1 rectangle floor

1 inclined rectangle front side

to get the length of the baseline (Hypotenuse) of the right-angled triangles on the side. we use Pythagoras

c² = a² + b²

where c is the Hypotenuse (the side opposite of the 90° angle).

c² = 3² + 4² = 9 + 16 = 25

c = 5

so, now, we have everything we need.

the area of a triangle side (since it is right-angled) :

4×3/2 = 6

2 sides, that makes 12

the area of the back side

6×3 = 18

the area of the floor

6×4 = 24

the area of the inclined front side

6×5 = 30

so, the total surface area is

12+18+24+30 = 84

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3 years ago

In MON, J, K, and L are midpoints. If JL = 11, LK = 13, and ON = 20, and JL || MN, LK || MO, and JK || ON, what is the length of

In-s [12.5K]

Answer:

The lengths of MN is 22 units, MO is 26 units and JK is 10 units

Step-by-step explanation:

A line segment joining the mid-points of two sides in a triangle is parallel to the third side and equal to half its length

In Δ MON

∵ J, K, and L are mid-points

∵ JL // MN and LK // MO

∴ L is the mid-point of ON

∴ J is the mid-point of MO

∴ K is the mid-point of MN

∵ J, L are the mid-points of MO and ON

∵ JL is opposite to MN

→ By using the rule above

∴ JL = $\frac{1}{2}$ MN

∵ JL = 11 units

∴ 11 = $\frac{1}{2}$ MN

→ Multiply both sides by 2

∴ 22 = MN

∴ MN = 22 units

∵ K, L are the mid-points of MN and ON

∵ KL is opposite to MO

→ By using the rule above

∴ KL = $\frac{1}{2}$ MO

∵ KL = 13 units

∴ 13 = $\frac{1}{2}$ MO

→ Multiply both sides by 2

∴ 26 = MO

∴ MO = 26 units

∵ J, K are the mid-points of MO and MN

∵ JK is opposite to ON

→ By using the rule above

∴ JK = $\frac{1}{2}$ ON

∵ ON =20 units

∴ JK = $\frac{1}{2}$ (20)

∴ JK = 10 units

∴ The lengths of MN are 22 units, MO is 26 units and JK is 10 units

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