Please answer before Monday 9 a.m.I have to go to school that day at that time.

Mathematics

1 answer:

xeze [42]3 years ago

6 0

Answer:

First choice, 984 cm²

Explanation:

The plastic pencil case has form of a triangular prism.

This triangular prism has five faces:

Top and bottom faces: two congruent triangles with a 10 cm base and 12 cm height.

Lateral faces: two congruent rectangles with a 24 cm length and 13 cm widht, and one rectangle with 24 cm length and 10 cm widht.

Surface area:

Top and bottom triangles:

area = (1/2) base × height

area of one triangle = 10 cm × 12 cm × (1/2) = 60 cm²

area of the two triangles = 2 × 60 cm² = 120 cm²

Lateral rectangles:

area of a rectangle = length × width

area of the trhee triangles = 24 cm × 10 cm + 2 × 24 cm × 13 cm = 240 cm² + 624 cm² = 864 cm².

Total area: 120 cm² + 864 cm² = 984 cm²

Answer: first choice, 984 cm²

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<h2>Explanation:</h2>

In every rectangle, the two diagonals have the same length. If a quadrilateral's diagonals have the same length, that doesn't mean it has to be a rectangle, but if a parallelogram's diagonals have the same length, then it's definitely a rectangle.

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$A(-1,3) \\ \\ B(1,5) \\ \\ C(5,1) \\ \\ D(3,-1)$

First pair of opposite sides:

Slope:

$\text{For AB}: \\ \\ m=\frac{5-3}{1-(-1)}=1 \\ \\ \\ \text{For CD}: \\ \\ m=\frac{1-(-1)}{5-3}=1 \\ \\ \\ \text{So AB and CD are parallel}$

Second pair of opposite sides:

Slope:

$\text{For BC}: \\ \\ m=\frac{1-5}{5-1}=-1 \\ \\ \\ \text{For AD}: \\ \\ m=\frac{-1-3}{3-(-1)}=-1 \\ \\ \\ \text{So BC and AD are parallel}$

So in fact this is a parallelogram. The other thing we need to prove is that the diagonals measure the same. Using distance formula:

$d=\sqrt{(y_{2}-y_{1})^2+(x_{2}-x_{1})^2} \\ \\ \\ Diagonal \ BD: \\ \\ d=\sqrt{(5-(-1))^2+(1-3)^2}=2\sqrt{10} \\ \\ \\ Diagonal \ AC: \\ \\ d=\sqrt{(3-1)^2+(-5-1)^2}=2\sqrt{10} \\ \\ \\$