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Valentin [98]
3 years ago
13

The length of a diagonal of a square is 7.5 mm. Find the area of the square.

Mathematics
1 answer:
dexar [7]3 years ago
7 0
By Pythagoreans' theorem,

7.5² = l² × b²
56.25 = l² × b²

Since l = b
56.25 ÷ 2
= l²/b²
= 28.125 mm

∴ l = √28.125
= 5.3033 mm

Area of square
= √28.125 × √28.125
= 28.125 mm²
≈ 28.1 mm² (3s.f.)
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svetlana [45]

Answer:

See Below.

Step-by-step explanation:

Statements:                                              Reasons:

1)\, XY=XZ                                              Given

2) \text{ $ m\angle Y= m\angle Z$}                                        Isosceles Triangle Theorem

\displaystyle 3) \text{ $m\angle Y=m\angle XYQ + \angle QYZ$}                  Angle Addition

\displaystyle 4)\text{ $YQ$ bisects $\angle XYZ$}                               Given

5) \text{ $m\angle XYQ=m\angle QYZ$}                           Definition of Bisector

\displaystyle 6)\text{ $m\angle Y=2m\angle QYZ$}                               Substitution

7)\text{ $m\angle Z=m\angle XZP+m\angle PZY$}              Angle Addition

8)\text{ $ZP$ bisects $\angle XZY$}                              Given

\displaystyle 9) \text{ $m\angle XZP=m\angle PZY$ }                          Definition of Bisector

\displaystyle 10) \text{ $ m\angle Z = 2m\angle PZY $}                            Substitution

11)\text{ } 2m\angle QYZ=2m\angle PZY                    Substitution

12)\text{ }m\angle QYZ=m\angle PZY                        Division Property of Equality

13)\text{ } YZ=YZ                                         Reflexive Property

14)\text{ } \Delta YZP\cong\Delta ZYQ                             Angle-Side-Angle Congruence*

15)\text{ } YQ=ZP                                         CPCTC

*For clarification:

∠Y = ∠Z

YZ = YZ (or ZY)

∠PZY = ∠QYZ

So, Angle-Side-Angle Congruence:

ΔYZP is congruent to ΔZYQ

5 0
3 years ago
Read 2 more answers
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myrzilka [38]

Answer:

690 sq in

Step-by-step explanation:

SA = LA + 2B     where LA is the lateral area and B is the area of the base

The triangular base has an area of

B = 1/2bh 1/2(5)(12) = 30

LA = ph  where p is the perimeter of the base and h is the height of the prism

LA = (12 + 5 + 13)(21) = 30(21) = 630

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3 0
3 years ago
Evaluate [(40 + 5) - 3^2] divided by 9 times 2
Irina-Kira [14]
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3 0
3 years ago
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Aloiza [94]
The answer to the math question

5 0
3 years ago
Can u please find the length of BC round to the nearest tenth
PolarNik [594]

Answer:

Step-by-step explanation:

Using sine rule

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A = 84° a = BC, C = 51°, c = 16

Sin84/BC = Sin51/16

Cross multiply

BC Sin51 = 16 × Sin84

BC = 15.91/Sin51

BC = 20.48unit

5 0
3 years ago
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